text: /* dhgeqz.f -- translated by f2c (version 20061008).
     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"
  #include "blaswrap.h"
  
  /* Table of constant values */
  
  static doublereal c_b12 = 0.;
  static doublereal c_b13 = 1.;
  static integer c__1 = 1;
  static integer c__3 = 3;
  
  /* Subroutine */ int dhgeqz_(char *job, char *compq, char *compz, integer *n, 
  	integer *ilo, integer *ihi, doublereal *h__, integer *ldh, doublereal 
  	*t, integer *ldt, doublereal *alphar, doublereal *alphai, doublereal *
  	beta, doublereal *q, integer *ldq, doublereal *z__, integer *ldz, 
  	doublereal *work, integer *lwork, integer *info)
  {
      /* System generated locals */
      integer h_dim1, h_offset, q_dim1, q_offset, t_dim1, t_offset, z_dim1, 
  	    z_offset, i__1, i__2, i__3, i__4;
      doublereal d__1, d__2, d__3, d__4;
  
      /* Builtin functions */
      double sqrt(doublereal);
  
      /* Local variables */
      doublereal c__;
      integer j;
      doublereal s, v[3], s1, s2, t1, u1, u2, a11, a12, a21, a22, b11, b22, c12,
  	     c21;
      integer jc;
      doublereal an, bn, cl, cq, cr;
      integer in;
      doublereal u12, w11, w12, w21;
      integer jr;
      doublereal cz, w22, sl, wi, sr, vs, wr, b1a, b2a, a1i, a2i, b1i, b2i, a1r,
  	     a2r, b1r, b2r, wr2, ad11, ad12, ad21, ad22, c11i, c22i;
      integer jch;
      doublereal c11r, c22r;
      logical ilq;
      doublereal u12l, tau, sqi;
      logical ilz;
      doublereal ulp, sqr, szi, szr, ad11l, ad12l, ad21l, ad22l, ad32l, wabs, 
  	    atol, btol, temp;
      extern /* Subroutine */ int drot_(integer *, doublereal *, integer *, 
  	    doublereal *, integer *, doublereal *, doublereal *), dlag2_(
  	    doublereal *, integer *, doublereal *, integer *, doublereal *, 
  	    doublereal *, doublereal *, doublereal *, doublereal *, 
  	    doublereal *);
      doublereal temp2, s1inv, scale;
      extern logical lsame_(char *, char *);
      integer iiter, ilast, jiter;
      doublereal anorm, bnorm;
      integer maxit;
      doublereal tempi, tempr;
      extern doublereal dlapy2_(doublereal *, doublereal *), dlapy3_(doublereal 
  	    *, doublereal *, doublereal *);
      extern /* Subroutine */ int dlasv2_(doublereal *, doublereal *, 
  	    doublereal *, doublereal *, doublereal *, doublereal *, 
  	    doublereal *, doublereal *, doublereal *);
      logical ilazr2;
      doublereal ascale, bscale;
      extern doublereal dlamch_(char *);
      extern /* Subroutine */ int dlarfg_(integer *, doublereal *, doublereal *, 
  	     integer *, doublereal *);
      extern doublereal dlanhs_(char *, integer *, doublereal *, integer *, 
  	    doublereal *);
      extern /* Subroutine */ int dlaset_(char *, integer *, integer *, 
  	    doublereal *, doublereal *, doublereal *, integer *);
      doublereal safmin;
      extern /* Subroutine */ int dlartg_(doublereal *, doublereal *, 
  	    doublereal *, doublereal *, doublereal *);
      doublereal safmax;
      extern /* Subroutine */ int xerbla_(char *, integer *);
      doublereal eshift;
      logical ilschr;
      integer icompq, ilastm, ischur;
      logical ilazro;
      integer icompz, ifirst, ifrstm, istart;
      logical ilpivt, lquery;
  
  
  /*  -- LAPACK routine (version 3.2.1)                                  -- */
  /*  -- LAPACK is a software package provided by Univ. of Tennessee,    -- */
  /*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
  /*  -- April 2009                                                      -- */
  
  /*     .. Scalar Arguments .. */
  /*     .. */
  /*     .. Array Arguments .. */
  /*     .. */
  
  /*  Purpose */
  /*  ======= */
  
  /*  DHGEQZ computes the eigenvalues of a real matrix pair (H,T), */
  /*  where H is an upper Hessenberg matrix and T is upper triangular, */
  /*  using the double-shift QZ method. */
  /*  Matrix pairs of this type are produced by the reduction to */
  /*  generalized upper Hessenberg form of a real matrix pair (A,B): */
  
  /*     A = Q1*H*Z1**T,  B = Q1*T*Z1**T, */
  
  /*  as computed by DGGHRD. */
  
  /*  If JOB='S', then the Hessenberg-triangular pair (H,T) is */
  /*  also reduced to generalized Schur form, */
  
  /*     H = Q*S*Z**T,  T = Q*P*Z**T, */
  
  /*  where Q and Z are orthogonal matrices, P is an upper triangular */
  /*  matrix, and S is a quasi-triangular matrix with 1-by-1 and 2-by-2 */
  /*  diagonal blocks. */
  
  /*  The 1-by-1 blocks correspond to real eigenvalues of the matrix pair */
  /*  (H,T) and the 2-by-2 blocks correspond to complex conjugate pairs of */
  /*  eigenvalues. */
  
  /*  Additionally, the 2-by-2 upper triangular diagonal blocks of P */
  /*  corresponding to 2-by-2 blocks of S are reduced to positive diagonal */
  /*  form, i.e., if S(j+1,j) is non-zero, then P(j+1,j) = P(j,j+1) = 0, */
  /*  P(j,j) > 0, and P(j+1,j+1) > 0. */
  
  /*  Optionally, the orthogonal matrix Q from the generalized Schur */
  /*  factorization may be postmultiplied into an input matrix Q1, and the */
  /*  orthogonal matrix Z may be postmultiplied into an input matrix Z1. */
  /*  If Q1 and Z1 are the orthogonal matrices from DGGHRD that reduced */
  /*  the matrix pair (A,B) to generalized upper Hessenberg form, then the */
  /*  output matrices Q1*Q and Z1*Z are the orthogonal factors from the */
  /*  generalized Schur factorization of (A,B): */
  
  /*     A = (Q1*Q)*S*(Z1*Z)**T,  B = (Q1*Q)*P*(Z1*Z)**T. */
  
  /*  To avoid overflow, eigenvalues of the matrix pair (H,T) (equivalently, */
  /*  of (A,B)) are computed as a pair of values (alpha,beta), where alpha is */
  /*  complex and beta real. */
  /*  If beta is nonzero, lambda = alpha / beta is an eigenvalue of the */
  /*  generalized nonsymmetric eigenvalue problem (GNEP) */
  /*     A*x = lambda*B*x */
  /*  and if alpha is nonzero, mu = beta / alpha is an eigenvalue of the */
  /*  alternate form of the GNEP */
  /*     mu*A*y = B*y. */
  /*  Real eigenvalues can be read directly from the generalized Schur */
  /*  form: */
  /*    alpha = S(i,i), beta = P(i,i). */
  
  /*  Ref: C.B. Moler & G.W. Stewart, "An Algorithm for Generalized Matrix */
  /*       Eigenvalue Problems", SIAM J. Numer. Anal., 10(1973), */
  /*       pp. 241--256. */
  
  /*  Arguments */
  /*  ========= */
  
  /*  JOB     (input) CHARACTER*1 */
  /*          = 'E': Compute eigenvalues only; */
  /*          = 'S': Compute eigenvalues and the Schur form. */
  
  /*  COMPQ   (input) CHARACTER*1 */
  /*          = 'N': Left Schur vectors (Q) are not computed; */
  /*          = 'I': Q is initialized to the unit matrix and the matrix Q */
  /*                 of left Schur vectors of (H,T) is returned; */
  /*          = 'V': Q must contain an orthogonal matrix Q1 on entry and */
  /*                 the product Q1*Q is returned. */
  
  /*  COMPZ   (input) CHARACTER*1 */
  /*          = 'N': Right Schur vectors (Z) are not computed; */
  /*          = 'I': Z is initialized to the unit matrix and the matrix Z */
  /*                 of right Schur vectors of (H,T) is returned; */
  /*          = 'V': Z must contain an orthogonal matrix Z1 on entry and */
  /*                 the product Z1*Z is returned. */
  
  /*  N       (input) INTEGER */
  /*          The order of the matrices H, T, Q, and Z.  N >= 0. */
  
  /*  ILO     (input) INTEGER */
  /*  IHI     (input) INTEGER */
  /*          ILO and IHI mark the rows and columns of H which are in */
  /*          Hessenberg form.  It is assumed that A is already upper */
  /*          triangular in rows and columns 1:ILO-1 and IHI+1:N. */
  /*          If N > 0, 1 <= ILO <= IHI <= N; if N = 0, ILO=1 and IHI=0. */
  
  /*  H       (input/output) DOUBLE PRECISION array, dimension (LDH, N) */
  /*          On entry, the N-by-N upper Hessenberg matrix H. */
  /*          On exit, if JOB = 'S', H contains the upper quasi-triangular */
  /*          matrix S from the generalized Schur factorization; */
  /*          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) < 0. */
  /*          If JOB = 'E', the diagonal blocks of H match those of S, but */
  /*          the rest of H is unspecified. */
  
  /*  LDH     (input) INTEGER */
  /*          The leading dimension of the array H.  LDH >= max( 1, N ). */
  
  /*  T       (input/output) DOUBLE PRECISION array, dimension (LDT, N) */
  /*          On entry, the N-by-N upper triangular matrix T. */
  /*          On exit, if JOB = 'S', T contains the upper triangular */
  /*          matrix P from the generalized Schur factorization; */
  /*          2-by-2 diagonal blocks of P corresponding to 2-by-2 blocks of S */
  /*          are reduced to positive diagonal form, i.e., if H(j+1,j) is */
  /*          non-zero, then T(j+1,j) = T(j,j+1) = 0, T(j,j) > 0, and */
  /*          T(j+1,j+1) > 0. */
  /*          If JOB = 'E', the diagonal blocks of T match those of P, but */
  /*          the rest of T is unspecified. */
  
  /*  LDT     (input) INTEGER */
  /*          The leading dimension of the array T.  LDT >= max( 1, N ). */
  
  /*  ALPHAR  (output) DOUBLE PRECISION array, dimension (N) */
  /*          The real parts of each scalar alpha defining an eigenvalue */
  /*          of GNEP. */
  
  /*  ALPHAI  (output) DOUBLE PRECISION array, dimension (N) */
  /*          The imaginary parts of each scalar alpha defining an */
  /*          eigenvalue of GNEP. */
  /*          If ALPHAI(j) is zero, then the j-th eigenvalue is real; if */
  /*          positive, then the j-th and (j+1)-st eigenvalues are a */
  /*          complex conjugate pair, with ALPHAI(j+1) = -ALPHAI(j). */
  
  /*  BETA    (output) DOUBLE PRECISION array, dimension (N) */
  /*          The scalars beta that define the eigenvalues of GNEP. */
  /*          Together, the quantities alpha = (ALPHAR(j),ALPHAI(j)) and */
  /*          beta = BETA(j) represent the j-th eigenvalue of the matrix */
  /*          pair (A,B), in one of the forms lambda = alpha/beta or */
  /*          mu = beta/alpha.  Since either lambda or mu may overflow, */
  /*          they should not, in general, be computed. */
  
  /*  Q       (input/output) DOUBLE PRECISION array, dimension (LDQ, N) */
  /*          On entry, if COMPZ = 'V', the orthogonal matrix Q1 used in */
  /*          the reduction of (A,B) to generalized Hessenberg form. */
  /*          On exit, if COMPZ = 'I', the orthogonal matrix of left Schur */
  /*          vectors of (H,T), and if COMPZ = 'V', the orthogonal matrix */
  /*          of left Schur vectors of (A,B). */
  /*          Not referenced if COMPZ = 'N'. */
  
  /*  LDQ     (input) INTEGER */
  /*          The leading dimension of the array Q.  LDQ >= 1. */
  /*          If COMPQ='V' or 'I', then LDQ >= N. */
  
  /*  Z       (input/output) DOUBLE PRECISION array, dimension (LDZ, N) */
  /*          On entry, if COMPZ = 'V', the orthogonal matrix Z1 used in */
  /*          the reduction of (A,B) to generalized Hessenberg form. */
  /*          On exit, if COMPZ = 'I', the orthogonal matrix of */
  /*          right Schur vectors of (H,T), and if COMPZ = 'V', the */
  /*          orthogonal matrix of right Schur vectors of (A,B). */
  /*          Not referenced if COMPZ = 'N'. */
  
  /*  LDZ     (input) INTEGER */
  /*          The leading dimension of the array Z.  LDZ >= 1. */
  /*          If COMPZ='V' or 'I', then LDZ >= N. */
  
  /*  WORK    (workspace/output) DOUBLE PRECISION array, dimension (MAX(1,LWORK)) */
  /*          On exit, if INFO >= 0, WORK(1) returns the optimal LWORK. */
  
  /*  LWORK   (input) INTEGER */
  /*          The dimension of the array WORK.  LWORK >= max(1,N). */
  
  /*          If LWORK = -1, then a workspace query is assumed; the routine */
  /*          only calculates the optimal size of the WORK array, returns */
  /*          this value as the first entry of the WORK array, and no error */
  /*          message related to LWORK is issued by XERBLA. */
  
  /*  INFO    (output) INTEGER */
  /*          = 0: successful exit */
  /*          < 0: if INFO = -i, the i-th argument had an illegal value */
  /*          = 1,...,N: the QZ iteration did not converge.  (H,T) is not */
  /*                     in Schur form, but ALPHAR(i), ALPHAI(i), and */
  /*                     BETA(i), i=INFO+1,...,N should be correct. */
  /*          = N+1,...,2*N: the shift calculation failed.  (H,T) is not */
  /*                     in Schur form, but ALPHAR(i), ALPHAI(i), and */
  /*                     BETA(i), i=INFO-N+1,...,N should be correct. */
  
  /*  Further Details */
  /*  =============== */
  
  /*  Iteration counters: */
  
  /*  JITER  -- counts iterations. */
  /*  IITER  -- counts iterations run since ILAST was last */
  /*            changed.  This is therefore reset only when a 1-by-1 or */
  /*            2-by-2 block deflates off the bottom. */
  
  /*  ===================================================================== */
  
  /*     .. Parameters .. */
  /*    $                     SAFETY = 1.0E+0 ) */
  /*     .. */
  /*     .. Local Scalars .. */
  /*     .. */
  /*     .. Local Arrays .. */
  /*     .. */
  /*     .. External Functions .. */
  /*     .. */
  /*     .. External Subroutines .. */
  /*     .. */
  /*     .. Intrinsic Functions .. */
  /*     .. */
  /*     .. Executable Statements .. */
  
  /*     Decode JOB, COMPQ, COMPZ */
  
      /* Parameter adjustments */
      h_dim1 = *ldh;
      h_offset = 1 + h_dim1;
      h__ -= h_offset;
      t_dim1 = *ldt;
      t_offset = 1 + t_dim1;
      t -= t_offset;
      --alphar;
      --alphai;
      --beta;
      q_dim1 = *ldq;
      q_offset = 1 + q_dim1;
      q -= q_offset;
      z_dim1 = *ldz;
      z_offset = 1 + z_dim1;
      z__ -= z_offset;
      --work;
  
      /* Function Body */
      if (lsame_(job, "E")) {
  	ilschr = FALSE_;
  	ischur = 1;
      } else if (lsame_(job, "S")) {
  	ilschr = TRUE_;
  	ischur = 2;
      } else {
  	ischur = 0;
      }
  
      if (lsame_(compq, "N")) {
  	ilq = FALSE_;
  	icompq = 1;
      } else if (lsame_(compq, "V")) {
  	ilq = TRUE_;
  	icompq = 2;
      } else if (lsame_(compq, "I")) {
  	ilq = TRUE_;
  	icompq = 3;
      } else {
  	icompq = 0;
      }
  
      if (lsame_(compz, "N")) {
  	ilz = FALSE_;
  	icompz = 1;
      } else if (lsame_(compz, "V")) {
  	ilz = TRUE_;
  	icompz = 2;
      } else if (lsame_(compz, "I")) {
  	ilz = TRUE_;
  	icompz = 3;
      } else {
  	icompz = 0;
      }
  
  /*     Check Argument Values */
  
      *info = 0;
      work[1] = (doublereal) max(1,*n);
      lquery = *lwork == -1;
      if (ischur == 0) {
  	*info = -1;
      } else if (icompq == 0) {
  	*info = -2;
      } else if (icompz == 0) {
  	*info = -3;
      } else if (*n < 0) {
  	*info = -4;
      } else if (*ilo < 1) {
  	*info = -5;
      } else if (*ihi > *n || *ihi < *ilo - 1) {
  	*info = -6;
      } else if (*ldh < *n) {
  	*info = -8;
      } else if (*ldt < *n) {
  	*info = -10;
      } else if (*ldq < 1 || ilq && *ldq < *n) {
  	*info = -15;
      } else if (*ldz < 1 || ilz && *ldz < *n) {
  	*info = -17;
      } else if (*lwork < max(1,*n) && ! lquery) {
  	*info = -19;
      }
      if (*info != 0) {
  	i__1 = -(*info);
  	xerbla_("DHGEQZ", &i__1);
  	return 0;
      } else if (lquery) {
  	return 0;
      }
  
  /*     Quick return if possible */
  
      if (*n <= 0) {
  	work[1] = 1.;
  	return 0;
      }
  
  /*     Initialize Q and Z */
  
      if (icompq == 3) {
  	dlaset_("Full", n, n, &c_b12, &c_b13, &q[q_offset], ldq);
      }
      if (icompz == 3) {
  	dlaset_("Full", n, n, &c_b12, &c_b13, &z__[z_offset], ldz);
      }
  
  /*     Machine Constants */
  
      in = *ihi + 1 - *ilo;
      safmin = dlamch_("S");
      safmax = 1. / safmin;
      ulp = dlamch_("E") * dlamch_("B");
      anorm = dlanhs_("F", &in, &h__[*ilo + *ilo * h_dim1], ldh, &work[1]);
      bnorm = dlanhs_("F", &in, &t[*ilo + *ilo * t_dim1], ldt, &work[1]);
  /* Computing MAX */
      d__1 = safmin, d__2 = ulp * anorm;
      atol = max(d__1,d__2);
  /* Computing MAX */
      d__1 = safmin, d__2 = ulp * bnorm;
      btol = max(d__1,d__2);
      ascale = 1. / max(safmin,anorm);
      bscale = 1. / max(safmin,bnorm);
  
  /*     Set Eigenvalues IHI+1:N */
  
      i__1 = *n;
      for (j = *ihi + 1; j <= i__1; ++j) {
  	if (t[j + j * t_dim1] < 0.) {
  	    if (ilschr) {
  		i__2 = j;
  		for (jr = 1; jr <= i__2; ++jr) {
  		    h__[jr + j * h_dim1] = -h__[jr + j * h_dim1];
  		    t[jr + j * t_dim1] = -t[jr + j * t_dim1];
  /* L10: */
  		}
  	    } else {
  		h__[j + j * h_dim1] = -h__[j + j * h_dim1];
  		t[j + j * t_dim1] = -t[j + j * t_dim1];
  	    }
  	    if (ilz) {
  		i__2 = *n;
  		for (jr = 1; jr <= i__2; ++jr) {
  		    z__[jr + j * z_dim1] = -z__[jr + j * z_dim1];
  /* L20: */
  		}
  	    }
  	}
  	alphar[j] = h__[j + j * h_dim1];
  	alphai[j] = 0.;
  	beta[j] = t[j + j * t_dim1];
  /* L30: */
      }
  
  /*     If IHI < ILO, skip QZ steps */
  
      if (*ihi < *ilo) {
  	goto L380;
      }
  
  /*     MAIN QZ ITERATION LOOP */
  
  /*     Initialize dynamic indices */
  
  /*     Eigenvalues ILAST+1:N have been found. */
  /*        Column operations modify rows IFRSTM:whatever. */
  /*        Row operations modify columns whatever:ILASTM. */
  
  /*     If only eigenvalues are being computed, then */
  /*        IFRSTM is the row of the last splitting row above row ILAST; */
  /*        this is always at least ILO. */
  /*     IITER counts iterations since the last eigenvalue was found, */
  /*        to tell when to use an extraordinary shift. */
  /*     MAXIT is the maximum number of QZ sweeps allowed. */
  
      ilast = *ihi;
      if (ilschr) {
  	ifrstm = 1;
  	ilastm = *n;
      } else {
  	ifrstm = *ilo;
  	ilastm = *ihi;
      }
      iiter = 0;
      eshift = 0.;
      maxit = (*ihi - *ilo + 1) * 30;
  
      i__1 = maxit;
      for (jiter = 1; jiter <= i__1; ++jiter) {
  
  /*        Split the matrix if possible. */
  
  /*        Two tests: */
  /*           1: H(j,j-1)=0  or  j=ILO */
  /*           2: T(j,j)=0 */
  
  	if (ilast == *ilo) {
  
  /*           Special case: j=ILAST */
  
  	    goto L80;
  	} else {
  	    if ((d__1 = h__[ilast + (ilast - 1) * h_dim1], abs(d__1)) <= atol)
  		     {
  		h__[ilast + (ilast - 1) * h_dim1] = 0.;
  		goto L80;
  	    }
  	}
  
  	if ((d__1 = t[ilast + ilast * t_dim1], abs(d__1)) <= btol) {
  	    t[ilast + ilast * t_dim1] = 0.;
  	    goto L70;
  	}
  
  /*        General case: j<ILAST */
  
  	i__2 = *ilo;
  	for (j = ilast - 1; j >= i__2; --j) {
  
  /*           Test 1: for H(j,j-1)=0 or j=ILO */
  
  	    if (j == *ilo) {
  		ilazro = TRUE_;
  	    } else {
  		if ((d__1 = h__[j + (j - 1) * h_dim1], abs(d__1)) <= atol) {
  		    h__[j + (j - 1) * h_dim1] = 0.;
  		    ilazro = TRUE_;
  		} else {
  		    ilazro = FALSE_;
  		}
  	    }
  
  /*           Test 2: for T(j,j)=0 */
  
  	    if ((d__1 = t[j + j * t_dim1], abs(d__1)) < btol) {
  		t[j + j * t_dim1] = 0.;
  
  /*              Test 1a: Check for 2 consecutive small subdiagonals in A */
  
  		ilazr2 = FALSE_;
  		if (! ilazro) {
  		    temp = (d__1 = h__[j + (j - 1) * h_dim1], abs(d__1));
  		    temp2 = (d__1 = h__[j + j * h_dim1], abs(d__1));
  		    tempr = max(temp,temp2);
  		    if (tempr < 1. && tempr != 0.) {
  			temp /= tempr;
  			temp2 /= tempr;
  		    }
  		    if (temp * (ascale * (d__1 = h__[j + 1 + j * h_dim1], abs(
  			    d__1))) <= temp2 * (ascale * atol)) {
  			ilazr2 = TRUE_;
  		    }
  		}
  
  /*              If both tests pass (1 & 2), i.e., the leading diagonal */
  /*              element of B in the block is zero, split a 1x1 block off */
  /*              at the top. (I.e., at the J-th row/column) The leading */
  /*              diagonal element of the remainder can also be zero, so */
  /*              this may have to be done repeatedly. */
  
  		if (ilazro || ilazr2) {
  		    i__3 = ilast - 1;
  		    for (jch = j; jch <= i__3; ++jch) {
  			temp = h__[jch + jch * h_dim1];
  			dlartg_(&temp, &h__[jch + 1 + jch * h_dim1], &c__, &s, 
  				 &h__[jch + jch * h_dim1]);
  			h__[jch + 1 + jch * h_dim1] = 0.;
  			i__4 = ilastm - jch;
  			drot_(&i__4, &h__[jch + (jch + 1) * h_dim1], ldh, &
  				h__[jch + 1 + (jch + 1) * h_dim1], ldh, &c__, 
  				&s);
  			i__4 = ilastm - jch;
  			drot_(&i__4, &t[jch + (jch + 1) * t_dim1], ldt, &t[
  				jch + 1 + (jch + 1) * t_dim1], ldt, &c__, &s);
  			if (ilq) {
  			    drot_(n, &q[jch * q_dim1 + 1], &c__1, &q[(jch + 1)
  				     * q_dim1 + 1], &c__1, &c__, &s);
  			}
  			if (ilazr2) {
  			    h__[jch + (jch - 1) * h_dim1] *= c__;
  			}
  			ilazr2 = FALSE_;
  			if ((d__1 = t[jch + 1 + (jch + 1) * t_dim1], abs(d__1)
  				) >= btol) {
  			    if (jch + 1 >= ilast) {
  				goto L80;
  			    } else {
  				ifirst = jch + 1;
  				goto L110;
  			    }
  			}
  			t[jch + 1 + (jch + 1) * t_dim1] = 0.;
  /* L40: */
  		    }
  		    goto L70;
  		} else {
  
  /*                 Only test 2 passed -- chase the zero to T(ILAST,ILAST) */
  /*                 Then process as in the case T(ILAST,ILAST)=0 */
  
  		    i__3 = ilast - 1;
  		    for (jch = j; jch <= i__3; ++jch) {
  			temp = t[jch + (jch + 1) * t_dim1];
  			dlartg_(&temp, &t[jch + 1 + (jch + 1) * t_dim1], &c__, 
  				 &s, &t[jch + (jch + 1) * t_dim1]);
  			t[jch + 1 + (jch + 1) * t_dim1] = 0.;
  			if (jch < ilastm - 1) {
  			    i__4 = ilastm - jch - 1;
  			    drot_(&i__4, &t[jch + (jch + 2) * t_dim1], ldt, &
  				    t[jch + 1 + (jch + 2) * t_dim1], ldt, &
  				    c__, &s);
  			}
  			i__4 = ilastm - jch + 2;
  			drot_(&i__4, &h__[jch + (jch - 1) * h_dim1], ldh, &
  				h__[jch + 1 + (jch - 1) * h_dim1], ldh, &c__, 
  				&s);
  			if (ilq) {
  			    drot_(n, &q[jch * q_dim1 + 1], &c__1, &q[(jch + 1)
  				     * q_dim1 + 1], &c__1, &c__, &s);
  			}
  			temp = h__[jch + 1 + jch * h_dim1];
  			dlartg_(&temp, &h__[jch + 1 + (jch - 1) * h_dim1], &
  				c__, &s, &h__[jch + 1 + jch * h_dim1]);
  			h__[jch + 1 + (jch - 1) * h_dim1] = 0.;
  			i__4 = jch + 1 - ifrstm;
  			drot_(&i__4, &h__[ifrstm + jch * h_dim1], &c__1, &h__[
  				ifrstm + (jch - 1) * h_dim1], &c__1, &c__, &s)
  				;
  			i__4 = jch - ifrstm;
  			drot_(&i__4, &t[ifrstm + jch * t_dim1], &c__1, &t[
  				ifrstm + (jch - 1) * t_dim1], &c__1, &c__, &s)
  				;
  			if (ilz) {
  			    drot_(n, &z__[jch * z_dim1 + 1], &c__1, &z__[(jch 
  				    - 1) * z_dim1 + 1], &c__1, &c__, &s);
  			}
  /* L50: */
  		    }
  		    goto L70;
  		}
  	    } else if (ilazro) {
  
  /*              Only test 1 passed -- work on J:ILAST */
  
  		ifirst = j;
  		goto L110;
  	    }
  
  /*           Neither test passed -- try next J */
  
  /* L60: */
  	}
  
  /*        (Drop-through is "impossible") */
  
  	*info = *n + 1;
  	goto L420;
  
  /*        T(ILAST,ILAST)=0 -- clear H(ILAST,ILAST-1) to split off a */
  /*        1x1 block. */
  
  L70:
  	temp = h__[ilast + ilast * h_dim1];
  	dlartg_(&temp, &h__[ilast + (ilast - 1) * h_dim1], &c__, &s, &h__[
  		ilast + ilast * h_dim1]);
  	h__[ilast + (ilast - 1) * h_dim1] = 0.;
  	i__2 = ilast - ifrstm;
  	drot_(&i__2, &h__[ifrstm + ilast * h_dim1], &c__1, &h__[ifrstm + (
  		ilast - 1) * h_dim1], &c__1, &c__, &s);
  	i__2 = ilast - ifrstm;
  	drot_(&i__2, &t[ifrstm + ilast * t_dim1], &c__1, &t[ifrstm + (ilast - 
  		1) * t_dim1], &c__1, &c__, &s);
  	if (ilz) {
  	    drot_(n, &z__[ilast * z_dim1 + 1], &c__1, &z__[(ilast - 1) * 
  		    z_dim1 + 1], &c__1, &c__, &s);
  	}
  
  /*        H(ILAST,ILAST-1)=0 -- Standardize B, set ALPHAR, ALPHAI, */
  /*                              and BETA */
  
  L80:
  	if (t[ilast + ilast * t_dim1] < 0.) {
  	    if (ilschr) {
  		i__2 = ilast;
  		for (j = ifrstm; j <= i__2; ++j) {
  		    h__[j + ilast * h_dim1] = -h__[j + ilast * h_dim1];
  		    t[j + ilast * t_dim1] = -t[j + ilast * t_dim1];
  /* L90: */
  		}
  	    } else {
  		h__[ilast + ilast * h_dim1] = -h__[ilast + ilast * h_dim1];
  		t[ilast + ilast * t_dim1] = -t[ilast + ilast * t_dim1];
  	    }
  	    if (ilz) {
  		i__2 = *n;
  		for (j = 1; j <= i__2; ++j) {
  		    z__[j + ilast * z_dim1] = -z__[j + ilast * z_dim1];
  /* L100: */
  		}
  	    }
  	}
  	alphar[ilast] = h__[ilast + ilast * h_dim1];
  	alphai[ilast] = 0.;
  	beta[ilast] = t[ilast + ilast * t_dim1];
  
  /*        Go to next block -- exit if finished. */
  
  	--ilast;
  	if (ilast < *ilo) {
  	    goto L380;
  	}
  
  /*        Reset counters */
  
  	iiter = 0;
  	eshift = 0.;
  	if (! ilschr) {
  	    ilastm = ilast;
  	    if (ifrstm > ilast) {
  		ifrstm = *ilo;
  	    }
  	}
  	goto L350;
  
  /*        QZ step */
  
  /*        This iteration only involves rows/columns IFIRST:ILAST. We */
  /*        assume IFIRST < ILAST, and that the diagonal of B is non-zero. */
  
  L110:
  	++iiter;
  	if (! ilschr) {
  	    ifrstm = ifirst;
  	}
  
  /*        Compute single shifts. */
  
  /*        At this point, IFIRST < ILAST, and the diagonal elements of */
  /*        T(IFIRST:ILAST,IFIRST,ILAST) are larger than BTOL (in */
  /*        magnitude) */
  
  	if (iiter / 10 * 10 == iiter) {
  
  /*           Exceptional shift.  Chosen for no particularly good reason. */
  /*           (Single shift only.) */
  
  	    if ((doublereal) maxit * safmin * (d__1 = h__[ilast - 1 + ilast * 
  		    h_dim1], abs(d__1)) < (d__2 = t[ilast - 1 + (ilast - 1) * 
  		    t_dim1], abs(d__2))) {
  		eshift += h__[ilast - 1 + ilast * h_dim1] / t[ilast - 1 + (
  			ilast - 1) * t_dim1];
  	    } else {
  		eshift += 1. / (safmin * (doublereal) maxit);
  	    }
  	    s1 = 1.;
  	    wr = eshift;
  
  	} else {
  
  /*           Shifts based on the generalized eigenvalues of the */
  /*           bottom-right 2x2 block of A and B. The first eigenvalue */
  /*           returned by DLAG2 is the Wilkinson shift (AEP p.512), */
  
  	    d__1 = safmin * 100.;
  	    dlag2_(&h__[ilast - 1 + (ilast - 1) * h_dim1], ldh, &t[ilast - 1 
  		    + (ilast - 1) * t_dim1], ldt, &d__1, &s1, &s2, &wr, &wr2, 
  		    &wi);
  
  /* Computing MAX */
  /* Computing MAX */
  	    d__3 = 1., d__4 = abs(wr), d__3 = max(d__3,d__4), d__4 = abs(wi);
  	    d__1 = s1, d__2 = safmin * max(d__3,d__4);
  	    temp = max(d__1,d__2);
  	    if (wi != 0.) {
  		goto L200;
  	    }
  	}
  
  /*        Fiddle with shift to avoid overflow */
  
  	temp = min(ascale,1.) * (safmax * .5);
  	if (s1 > temp) {
  	    scale = temp / s1;
  	} else {
  	    scale = 1.;
  	}
  
  	temp = min(bscale,1.) * (safmax * .5);
  	if (abs(wr) > temp) {
  /* Computing MIN */
  	    d__1 = scale, d__2 = temp / abs(wr);
  	    scale = min(d__1,d__2);
  	}
  	s1 = scale * s1;
  	wr = scale * wr;
  
  /*        Now check for two consecutive small subdiagonals. */
  
  	i__2 = ifirst + 1;
  	for (j = ilast - 1; j >= i__2; --j) {
  	    istart = j;
  	    temp = (d__1 = s1 * h__[j + (j - 1) * h_dim1], abs(d__1));
  	    temp2 = (d__1 = s1 * h__[j + j * h_dim1] - wr * t[j + j * t_dim1],
  		     abs(d__1));
  	    tempr = max(temp,temp2);
  	    if (tempr < 1. && tempr != 0.) {
  		temp /= tempr;
  		temp2 /= tempr;
  	    }
  	    if ((d__1 = ascale * h__[j + 1 + j * h_dim1] * temp, abs(d__1)) <=
  		     ascale * atol * temp2) {
  		goto L130;
  	    }
  /* L120: */
  	}
  
  	istart = ifirst;
  L130:
  
  /*        Do an implicit single-shift QZ sweep. */
  
  /*        Initial Q */
  
  	temp = s1 * h__[istart + istart * h_dim1] - wr * t[istart + istart * 
  		t_dim1];
  	temp2 = s1 * h__[istart + 1 + istart * h_dim1];
  	dlartg_(&temp, &temp2, &c__, &s, &tempr);
  
  /*        Sweep */
  
  	i__2 = ilast - 1;
  	for (j = istart; j <= i__2; ++j) {
  	    if (j > istart) {
  		temp = h__[j + (j - 1) * h_dim1];
  		dlartg_(&temp, &h__[j + 1 + (j - 1) * h_dim1], &c__, &s, &h__[
  			j + (j - 1) * h_dim1]);
  		h__[j + 1 + (j - 1) * h_dim1] = 0.;
  	    }
  
  	    i__3 = ilastm;
  	    for (jc = j; jc <= i__3; ++jc) {
  		temp = c__ * h__[j + jc * h_dim1] + s * h__[j + 1 + jc * 
  			h_dim1];
  		h__[j + 1 + jc * h_dim1] = -s * h__[j + jc * h_dim1] + c__ * 
  			h__[j + 1 + jc * h_dim1];
  		h__[j + jc * h_dim1] = temp;
  		temp2 = c__ * t[j + jc * t_dim1] + s * t[j + 1 + jc * t_dim1];
  		t[j + 1 + jc * t_dim1] = -s * t[j + jc * t_dim1] + c__ * t[j 
  			+ 1 + jc * t_dim1];
  		t[j + jc * t_dim1] = temp2;
  /* L140: */
  	    }
  	    if (ilq) {
  		i__3 = *n;
  		for (jr = 1; jr <= i__3; ++jr) {
  		    temp = c__ * q[jr + j * q_dim1] + s * q[jr + (j + 1) * 
  			    q_dim1];
  		    q[jr + (j + 1) * q_dim1] = -s * q[jr + j * q_dim1] + c__ *
  			     q[jr + (j + 1) * q_dim1];
  		    q[jr + j * q_dim1] = temp;
  /* L150: */
  		}
  	    }
  
  	    temp = t[j + 1 + (j + 1) * t_dim1];
  	    dlartg_(&temp, &t[j + 1 + j * t_dim1], &c__, &s, &t[j + 1 + (j + 
  		    1) * t_dim1]);
  	    t[j + 1 + j * t_dim1] = 0.;
  
  /* Computing MIN */
  	    i__4 = j + 2;
  	    i__3 = min(i__4,ilast);
  	    for (jr = ifrstm; jr <= i__3; ++jr) {
  		temp = c__ * h__[jr + (j + 1) * h_dim1] + s * h__[jr + j * 
  			h_dim1];
  		h__[jr + j * h_dim1] = -s * h__[jr + (j + 1) * h_dim1] + c__ *
  			 h__[jr + j * h_dim1];
  		h__[jr + (j + 1) * h_dim1] = temp;
  /* L160: */
  	    }
  	    i__3 = j;
  	    for (jr = ifrstm; jr <= i__3; ++jr) {
  		temp = c__ * t[jr + (j + 1) * t_dim1] + s * t[jr + j * t_dim1]
  			;
  		t[jr + j * t_dim1] = -s * t[jr + (j + 1) * t_dim1] + c__ * t[
  			jr + j * t_dim1];
  		t[jr + (j + 1) * t_dim1] = temp;
  /* L170: */
  	    }
  	    if (ilz) {
  		i__3 = *n;
  		for (jr = 1; jr <= i__3; ++jr) {
  		    temp = c__ * z__[jr + (j + 1) * z_dim1] + s * z__[jr + j *
  			     z_dim1];
  		    z__[jr + j * z_dim1] = -s * z__[jr + (j + 1) * z_dim1] + 
  			    c__ * z__[jr + j * z_dim1];
  		    z__[jr + (j + 1) * z_dim1] = temp;
  /* L180: */
  		}
  	    }
  /* L190: */
  	}
  
  	goto L350;
  
  /*        Use Francis double-shift */
  
  /*        Note: the Francis double-shift should work with real shifts, */
  /*              but only if the block is at least 3x3. */
  /*              This code may break if this point is reached with */
  /*              a 2x2 block with real eigenvalues. */
  
  L200:
  	if (ifirst + 1 == ilast) {
  
  /*           Special case -- 2x2 block with complex eigenvectors */
  
  /*           Step 1: Standardize, that is, rotate so that */
  
  /*                       ( B11  0  ) */
  /*                   B = (         )  with B11 non-negative. */
  /*                       (  0  B22 ) */
  
  	    dlasv2_(&t[ilast - 1 + (ilast - 1) * t_dim1], &t[ilast - 1 + 
  		    ilast * t_dim1], &t[ilast + ilast * t_dim1], &b22, &b11, &
  		    sr, &cr, &sl, &cl);
  
  	    if (b11 < 0.) {
  		cr = -cr;
  		sr = -sr;
  		b11 = -b11;
  		b22 = -b22;
  	    }
  
  	    i__2 = ilastm + 1 - ifirst;
  	    drot_(&i__2, &h__[ilast - 1 + (ilast - 1) * h_dim1], ldh, &h__[
  		    ilast + (ilast - 1) * h_dim1], ldh, &cl, &sl);
  	    i__2 = ilast + 1 - ifrstm;
  	    drot_(&i__2, &h__[ifrstm + (ilast - 1) * h_dim1], &c__1, &h__[
  		    ifrstm + ilast * h_dim1], &c__1, &cr, &sr);
  
  	    if (ilast < ilastm) {
  		i__2 = ilastm - ilast;
  		drot_(&i__2, &t[ilast - 1 + (ilast + 1) * t_dim1], ldt, &t[
  			ilast + (ilast + 1) * t_dim1], ldt, &cl, &sl);
  	    }
  	    if (ifrstm < ilast - 1) {
  		i__2 = ifirst - ifrstm;
  		drot_(&i__2, &t[ifrstm + (ilast - 1) * t_dim1], &c__1, &t[
  			ifrstm + ilast * t_dim1], &c__1, &cr, &sr);
  	    }
  
  	    if (ilq) {
  		drot_(n, &q[(ilast - 1) * q_dim1 + 1], &c__1, &q[ilast * 
  			q_dim1 + 1], &c__1, &cl, &sl);
  	    }
  	    if (ilz) {
  		drot_(n, &z__[(ilast - 1) * z_dim1 + 1], &c__1, &z__[ilast * 
  			z_dim1 + 1], &c__1, &cr, &sr);
  	    }
  
  	    t[ilast - 1 + (ilast - 1) * t_dim1] = b11;
  	    t[ilast - 1 + ilast * t_dim1] = 0.;
  	    t[ilast + (ilast - 1) * t_dim1] = 0.;
  	    t[ilast + ilast * t_dim1] = b22;
  
  /*           If B22 is negative, negate column ILAST */
  
  	    if (b22 < 0.) {
  		i__2 = ilast;
  		for (j = ifrstm; j <= i__2; ++j) {
  		    h__[j + ilast * h_dim1] = -h__[j + ilast * h_dim1];
  		    t[j + ilast * t_dim1] = -t[j + ilast * t_dim1];
  /* L210: */
  		}
  
  		if (ilz) {
  		    i__2 = *n;
  		    for (j = 1; j <= i__2; ++j) {
  			z__[j + ilast * z_dim1] = -z__[j + ilast * z_dim1];
  /* L220: */
  		    }
  		}
  	    }
  
  /*           Step 2: Compute ALPHAR, ALPHAI, and BETA (see refs.) */
  
  /*           Recompute shift */
  
  	    d__1 = safmin * 100.;
  	    dlag2_(&h__[ilast - 1 + (ilast - 1) * h_dim1], ldh, &t[ilast - 1 
  		    + (ilast - 1) * t_dim1], ldt, &d__1, &s1, &temp, &wr, &
  		    temp2, &wi);
  
  /*           If standardization has perturbed the shift onto real line, */
  /*           do another (real single-shift) QR step. */
  
  	    if (wi == 0.) {
  		goto L350;
  	    }
  	    s1inv = 1. / s1;
  
  /*           Do EISPACK (QZVAL) computation of alpha and beta */
  
  	    a11 = h__[ilast - 1 + (ilast - 1) * h_dim1];
  	    a21 = h__[ilast + (ilast - 1) * h_dim1];
  	    a12 = h__[ilast - 1 + ilast * h_dim1];
  	    a22 = h__[ilast + ilast * h_dim1];
  
  /*           Compute complex Givens rotation on right */
  /*           (Assume some element of C = (sA - wB) > unfl ) */
  /*                            __ */
  /*           (sA - wB) ( CZ   -SZ ) */
  /*                     ( SZ    CZ ) */
  
  	    c11r = s1 * a11 - wr * b11;
  	    c11i = -wi * b11;
  	    c12 = s1 * a12;
  	    c21 = s1 * a21;
  	    c22r = s1 * a22 - wr * b22;
  	    c22i = -wi * b22;
  
  	    if (abs(c11r) + abs(c11i) + abs(c12) > abs(c21) + abs(c22r) + abs(
  		    c22i)) {
  		t1 = dlapy3_(&c12, &c11r, &c11i);
  		cz = c12 / t1;
  		szr = -c11r / t1;
  		szi = -c11i / t1;
  	    } else {
  		cz = dlapy2_(&c22r, &c22i);
  		if (cz <= safmin) {
  		    cz = 0.;
  		    szr = 1.;
  		    szi = 0.;
  		} else {
  		    tempr = c22r / cz;
  		    tempi = c22i / cz;
  		    t1 = dlapy2_(&cz, &c21);
  		    cz /= t1;
  		    szr = -c21 * tempr / t1;
  		    szi = c21 * tempi / t1;
  		}
  	    }
  
  /*           Compute Givens rotation on left */
  
  /*           (  CQ   SQ ) */
  /*           (  __      )  A or B */
  /*           ( -SQ   CQ ) */
  
  	    an = abs(a11) + abs(a12) + abs(a21) + abs(a22);
  	    bn = abs(b11) + abs(b22);
  	    wabs = abs(wr) + abs(wi);
  	    if (s1 * an > wabs * bn) {
  		cq = cz * b11;
  		sqr = szr * b22;
  		sqi = -szi * b22;
  	    } else {
  		a1r = cz * a11 + szr * a12;
  		a1i = szi * a12;
  		a2r = cz * a21 + szr * a22;
  		a2i = szi * a22;
  		cq = dlapy2_(&a1r, &a1i);
  		if (cq <= safmin) {
  		    cq = 0.;
  		    sqr = 1.;
  		    sqi = 0.;
  		} else {
  		    tempr = a1r / cq;
  		    tempi = a1i / cq;
  		    sqr = tempr * a2r + tempi * a2i;
  		    sqi = tempi * a2r - tempr * a2i;
  		}
  	    }
  	    t1 = dlapy3_(&cq, &sqr, &sqi);
  	    cq /= t1;
  	    sqr /= t1;
  	    sqi /= t1;
  
  /*           Compute diagonal elements of QBZ */
  
  	    tempr = sqr * szr - sqi * szi;
  	    tempi = sqr * szi + sqi * szr;
  	    b1r = cq * cz * b11 + tempr * b22;
  	    b1i = tempi * b22;
  	    b1a = dlapy2_(&b1r, &b1i);
  	    b2r = cq * cz * b22 + tempr * b11;
  	    b2i = -tempi * b11;
  	    b2a = dlapy2_(&b2r, &b2i);
  
  /*           Normalize so beta > 0, and Im( alpha1 ) > 0 */
  
  	    beta[ilast - 1] = b1a;
  	    beta[ilast] = b2a;
  	    alphar[ilast - 1] = wr * b1a * s1inv;
  	    alphai[ilast - 1] = wi * b1a * s1inv;
  	    alphar[ilast] = wr * b2a * s1inv;
  	    alphai[ilast] = -(wi * b2a) * s1inv;
  
  /*           Step 3: Go to next block -- exit if finished. */
  
  	    ilast = ifirst - 1;
  	    if (ilast < *ilo) {
  		goto L380;
  	    }
  
  /*           Reset counters */
  
  	    iiter = 0;
  	    eshift = 0.;
  	    if (! ilschr) {
  		ilastm = ilast;
  		if (ifrstm > ilast) {
  		    ifrstm = *ilo;
  		}
  	    }
  	    goto L350;
  	} else {
  
  /*           Usual case: 3x3 or larger block, using Francis implicit */
  /*                       double-shift */
  
  /*                                    2 */
  /*           Eigenvalue equation is  w  - c w + d = 0, */
  
  /*                                         -1 2        -1 */
  /*           so compute 1st column of  (A B  )  - c A B   + d */
  /*           using the formula in QZIT (from EISPACK) */
  
  /*           We assume that the block is at least 3x3 */
  
  	    ad11 = ascale * h__[ilast - 1 + (ilast - 1) * h_dim1] / (bscale * 
  		    t[ilast - 1 + (ilast - 1) * t_dim1]);
  	    ad21 = ascale * h__[ilast + (ilast - 1) * h_dim1] / (bscale * t[
  		    ilast - 1 + (ilast - 1) * t_dim1]);
  	    ad12 = ascale * h__[ilast - 1 + ilast * h_dim1] / (bscale * t[
  		    ilast + ilast * t_dim1]);
  	    ad22 = ascale * h__[ilast + ilast * h_dim1] / (bscale * t[ilast + 
  		    ilast * t_dim1]);
  	    u12 = t[ilast - 1 + ilast * t_dim1] / t[ilast + ilast * t_dim1];
  	    ad11l = ascale * h__[ifirst + ifirst * h_dim1] / (bscale * t[
  		    ifirst + ifirst * t_dim1]);
  	    ad21l = ascale * h__[ifirst + 1 + ifirst * h_dim1] / (bscale * t[
  		    ifirst + ifirst * t_dim1]);
  	    ad12l = ascale * h__[ifirst + (ifirst + 1) * h_dim1] / (bscale * 
  		    t[ifirst + 1 + (ifirst + 1) * t_dim1]);
  	    ad22l = ascale * h__[ifirst + 1 + (ifirst + 1) * h_dim1] / (
  		    bscale * t[ifirst + 1 + (ifirst + 1) * t_dim1]);
  	    ad32l = ascale * h__[ifirst + 2 + (ifirst + 1) * h_dim1] / (
  		    bscale * t[ifirst + 1 + (ifirst + 1) * t_dim1]);
  	    u12l = t[ifirst + (ifirst + 1) * t_dim1] / t[ifirst + 1 + (ifirst 
  		    + 1) * t_dim1];
  
  	    v[0] = (ad11 - ad11l) * (ad22 - ad11l) - ad12 * ad21 + ad21 * u12 
  		    * ad11l + (ad12l - ad11l * u12l) * ad21l;
  	    v[1] = (ad22l - ad11l - ad21l * u12l - (ad11 - ad11l) - (ad22 - 
  		    ad11l) + ad21 * u12) * ad21l;
  	    v[2] = ad32l * ad21l;
  
  	    istart = ifirst;
  
  	    dlarfg_(&c__3, v, &v[1], &c__1, &tau);
  	    v[0] = 1.;
  
  /*           Sweep */
  
  	    i__2 = ilast - 2;
  	    for (j = istart; j <= i__2; ++j) {
  
  /*              All but last elements: use 3x3 Householder transforms. */
  
  /*              Zero (j-1)st column of A */
  
  		if (j > istart) {
  		    v[0] = h__[j + (j - 1) * h_dim1];
  		    v[1] = h__[j + 1 + (j - 1) * h_dim1];
  		    v[2] = h__[j + 2 + (j - 1) * h_dim1];
  
  		    dlarfg_(&c__3, &h__[j + (j - 1) * h_dim1], &v[1], &c__1, &
  			    tau);
  		    v[0] = 1.;
  		    h__[j + 1 + (j - 1) * h_dim1] = 0.;
  		    h__[j + 2 + (j - 1) * h_dim1] = 0.;
  		}
  
  		i__3 = ilastm;
  		for (jc = j; jc <= i__3; ++jc) {
  		    temp = tau * (h__[j + jc * h_dim1] + v[1] * h__[j + 1 + 
  			    jc * h_dim1] + v[2] * h__[j + 2 + jc * h_dim1]);
  		    h__[j + jc * h_dim1] -= temp;
  		    h__[j + 1 + jc * h_dim1] -= temp * v[1];
  		    h__[j + 2 + jc * h_dim1] -= temp * v[2];
  		    temp2 = tau * (t[j + jc * t_dim1] + v[1] * t[j + 1 + jc * 
  			    t_dim1] + v[2] * t[j + 2 + jc * t_dim1]);
  		    t[j + jc * t_dim1] -= temp2;
  		    t[j + 1 + jc * t_dim1] -= temp2 * v[1];
  		    t[j + 2 + jc * t_dim1] -= temp2 * v[2];
  /* L230: */
  		}
  		if (ilq) {
  		    i__3 = *n;
  		    for (jr = 1; jr <= i__3; ++jr) {
  			temp = tau * (q[jr + j * q_dim1] + v[1] * q[jr + (j + 
  				1) * q_dim1] + v[2] * q[jr + (j + 2) * q_dim1]
  				);
  			q[jr + j * q_dim1] -= temp;
  			q[jr + (j + 1) * q_dim1] -= temp * v[1];
  			q[jr + (j + 2) * q_dim1] -= temp * v[2];
  /* L240: */
  		    }
  		}
  
  /*              Zero j-th column of B (see DLAGBC for details) */
  
  /*              Swap rows to pivot */
  
  		ilpivt = FALSE_;
  /* Computing MAX */
  		d__3 = (d__1 = t[j + 1 + (j + 1) * t_dim1], abs(d__1)), d__4 =
  			 (d__2 = t[j + 1 + (j + 2) * t_dim1], abs(d__2));
  		temp = max(d__3,d__4);
  /* Computing MAX */
  		d__3 = (d__1 = t[j + 2 + (j + 1) * t_dim1], abs(d__1)), d__4 =
  			 (d__2 = t[j + 2 + (j + 2) * t_dim1], abs(d__2));
  		temp2 = max(d__3,d__4);
  		if (max(temp,temp2) < safmin) {
  		    scale = 0.;
  		    u1 = 1.;
  		    u2 = 0.;
  		    goto L250;
  		} else if (temp >= temp2) {
  		    w11 = t[j + 1 + (j + 1) * t_dim1];
  		    w21 = t[j + 2 + (j + 1) * t_dim1];
  		    w12 = t[j + 1 + (j + 2) * t_dim1];
  		    w22 = t[j + 2 + (j + 2) * t_dim1];
  		    u1 = t[j + 1 + j * t_dim1];
  		    u2 = t[j + 2 + j * t_dim1];
  		} else {
  		    w21 = t[j + 1 + (j + 1) * t_dim1];
  		    w11 = t[j + 2 + (j + 1) * t_dim1];
  		    w22 = t[j + 1 + (j + 2) * t_dim1];
  		    w12 = t[j + 2 + (j + 2) * t_dim1];
  		    u2 = t[j + 1 + j * t_dim1];
  		    u1 = t[j + 2 + j * t_dim1];
  		}
  
  /*              Swap columns if nec. */
  
  		if (abs(w12) > abs(w11)) {
  		    ilpivt = TRUE_;
  		    temp = w12;
  		    temp2 = w22;
  		    w12 = w11;
  		    w22 = w21;
  		    w11 = temp;
  		    w21 = temp2;
  		}
  
  /*              LU-factor */
  
  		temp = w21 / w11;
  		u2 -= temp * u1;
  		w22 -= temp * w12;
  		w21 = 0.;
  
  /*              Compute SCALE */
  
  		scale = 1.;
  		if (abs(w22) < safmin) {
  		    scale = 0.;
  		    u2 = 1.;
  		    u1 = -w12 / w11;
  		    goto L250;
  		}
  		if (abs(w22) < abs(u2)) {
  		    scale = (d__1 = w22 / u2, abs(d__1));
  		}
  		if (abs(w11) < abs(u1)) {
  /* Computing MIN */
  		    d__2 = scale, d__3 = (d__1 = w11 / u1, abs(d__1));
  		    scale = min(d__2,d__3);
  		}
  
  /*              Solve */
  
  		u2 = scale * u2 / w22;
  		u1 = (scale * u1 - w12 * u2) / w11;
  
  L250:
  		if (ilpivt) {
  		    temp = u2;
  		    u2 = u1;
  		    u1 = temp;
  		}
  
  /*              Compute Householder Vector */
  
  /* Computing 2nd power */
  		d__1 = scale;
  /* Computing 2nd power */
  		d__2 = u1;
  /* Computing 2nd power */
  		d__3 = u2;
  		t1 = sqrt(d__1 * d__1 + d__2 * d__2 + d__3 * d__3);
  		tau = scale / t1 + 1.;
  		vs = -1. / (scale + t1);
  		v[0] = 1.;
  		v[1] = vs * u1;
  		v[2] = vs * u2;
  
  /*              Apply transformations from the right. */
  
  /* Computing MIN */
  		i__4 = j + 3;
  		i__3 = min(i__4,ilast);
  		for (jr = ifrstm; jr <= i__3; ++jr) {
  		    temp = tau * (h__[jr + j * h_dim1] + v[1] * h__[jr + (j + 
  			    1) * h_dim1] + v[2] * h__[jr + (j + 2) * h_dim1]);
  		    h__[jr + j * h_dim1] -= temp;
  		    h__[jr + (j + 1) * h_dim1] -= temp * v[1];
  		    h__[jr + (j + 2) * h_dim1] -= temp * v[2];
  /* L260: */
  		}
  		i__3 = j + 2;
  		for (jr = ifrstm; jr <= i__3; ++jr) {
  		    temp = tau * (t[jr + j * t_dim1] + v[1] * t[jr + (j + 1) *
  			     t_dim1] + v[2] * t[jr + (j + 2) * t_dim1]);
  		    t[jr + j * t_dim1] -= temp;
  		    t[jr + (j + 1) * t_dim1] -= temp * v[1];
  		    t[jr + (j + 2) * t_dim1] -= temp * v[2];
  /* L270: */
  		}
  		if (ilz) {
  		    i__3 = *n;
  		    for (jr = 1; jr <= i__3; ++jr) {
  			temp = tau * (z__[jr + j * z_dim1] + v[1] * z__[jr + (
  				j + 1) * z_dim1] + v[2] * z__[jr + (j + 2) * 
  				z_dim1]);
  			z__[jr + j * z_dim1] -= temp;
  			z__[jr + (j + 1) * z_dim1] -= temp * v[1];
  			z__[jr + (j + 2) * z_dim1] -= temp * v[2];
  /* L280: */
  		    }
  		}
  		t[j + 1 + j * t_dim1] = 0.;
  		t[j + 2 + j * t_dim1] = 0.;
  /* L290: */
  	    }
  
  /*           Last elements: Use Givens rotations */
  
  /*           Rotations from the left */
  
  	    j = ilast - 1;
  	    temp = h__[j + (j - 1) * h_dim1];
  	    dlartg_(&temp, &h__[j + 1 + (j - 1) * h_dim1], &c__, &s, &h__[j + 
  		    (j - 1) * h_dim1]);
  	    h__[j + 1 + (j - 1) * h_dim1] = 0.;
  
  	    i__2 = ilastm;
  	    for (jc = j; jc <= i__2; ++jc) {
  		temp = c__ * h__[j + jc * h_dim1] + s * h__[j + 1 + jc * 
  			h_dim1];
  		h__[j + 1 + jc * h_dim1] = -s * h__[j + jc * h_dim1] + c__ * 
  			h__[j + 1 + jc * h_dim1];
  		h__[j + jc * h_dim1] = temp;
  		temp2 = c__ * t[j + jc * t_dim1] + s * t[j + 1 + jc * t_dim1];
  		t[j + 1 + jc * t_dim1] = -s * t[j + jc * t_dim1] + c__ * t[j 
  			+ 1 + jc * t_dim1];
  		t[j + jc * t_dim1] = temp2;
  /* L300: */
  	    }
  	    if (ilq) {
  		i__2 = *n;
  		for (jr = 1; jr <= i__2; ++jr) {
  		    temp = c__ * q[jr + j * q_dim1] + s * q[jr + (j + 1) * 
  			    q_dim1];
  		    q[jr + (j + 1) * q_dim1] = -s * q[jr + j * q_dim1] + c__ *
  			     q[jr + (j + 1) * q_dim1];
  		    q[jr + j * q_dim1] = temp;
  /* L310: */
  		}
  	    }
  
  /*           Rotations from the right. */
  
  	    temp = t[j + 1 + (j + 1) * t_dim1];
  	    dlartg_(&temp, &t[j + 1 + j * t_dim1], &c__, &s, &t[j + 1 + (j + 
  		    1) * t_dim1]);
  	    t[j + 1 + j * t_dim1] = 0.;
  
  	    i__2 = ilast;
  	    for (jr = ifrstm; jr <= i__2; ++jr) {
  		temp = c__ * h__[jr + (j + 1) * h_dim1] + s * h__[jr + j * 
  			h_dim1];
  		h__[jr + j * h_dim1] = -s * h__[jr + (j + 1) * h_dim1] + c__ *
  			 h__[jr + j * h_dim1];
  		h__[jr + (j + 1) * h_dim1] = temp;
  /* L320: */
  	    }
  	    i__2 = ilast - 1;
  	    for (jr = ifrstm; jr <= i__2; ++jr) {
  		temp = c__ * t[jr + (j + 1) * t_dim1] + s * t[jr + j * t_dim1]
  			;
  		t[jr + j * t_dim1] = -s * t[jr + (j + 1) * t_dim1] + c__ * t[
  			jr + j * t_dim1];
  		t[jr + (j + 1) * t_dim1] = temp;
  /* L330: */
  	    }
  	    if (ilz) {
  		i__2 = *n;
  		for (jr = 1; jr <= i__2; ++jr) {
  		    temp = c__ * z__[jr + (j + 1) * z_dim1] + s * z__[jr + j *
  			     z_dim1];
  		    z__[jr + j * z_dim1] = -s * z__[jr + (j + 1) * z_dim1] + 
  			    c__ * z__[jr + j * z_dim1];
  		    z__[jr + (j + 1) * z_dim1] = temp;
  /* L340: */
  		}
  	    }
  
  /*           End of Double-Shift code */
  
  	}
  
  	goto L350;
  
  /*        End of iteration loop */
  
  L350:
  /* L360: */
  	;
      }
  
  /*     Drop-through = non-convergence */
  
      *info = ilast;
      goto L420;
  
  /*     Successful completion of all QZ steps */
  
  L380:
  
  /*     Set Eigenvalues 1:ILO-1 */
  
      i__1 = *ilo - 1;
      for (j = 1; j <= i__1; ++j) {
  	if (t[j + j * t_dim1] < 0.) {
  	    if (ilschr) {
  		i__2 = j;
  		for (jr = 1; jr <= i__2; ++jr) {
  		    h__[jr + j * h_dim1] = -h__[jr + j * h_dim1];
  		    t[jr + j * t_dim1] = -t[jr + j * t_dim1];
  /* L390: */
  		}
  	    } else {
  		h__[j + j * h_dim1] = -h__[j + j * h_dim1];
  		t[j + j * t_dim1] = -t[j + j * t_dim1];
  	    }
  	    if (ilz) {
  		i__2 = *n;
  		for (jr = 1; jr <= i__2; ++jr) {
  		    z__[jr + j * z_dim1] = -z__[jr + j * z_dim1];
  /* L400: */
  		}
  	    }
  	}
  	alphar[j] = h__[j + j * h_dim1];
  	alphai[j] = 0.;
  	beta[j] = t[j + j * t_dim1];
  /* L410: */
      }
  
  /*     Normal Termination */
  
      *info = 0;
  
  /*     Exit (other than argument error) -- return optimal workspace size */
  
  L420:
      work[1] = (doublereal) (*n);
      return 0;
  
  /*     End of DHGEQZ */
  
  } /* dhgeqz_ */
  