shgeqz.c

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/* shgeqz.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 real c_b12 = 0.f;
static real c_b13 = 1.f;
static integer c__1 = 1;
static integer c__3 = 3;

/* Subroutine */ int shgeqz_(char *job, char *compq, char *compz, integer *n, 
        integer *ilo, integer *ihi, real *h__, integer *ldh, real *t, integer 
        *ldt, real *alphar, real *alphai, real *beta, real *q, integer *ldq, 
        real *z__, integer *ldz, real *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;
    real r__1, r__2, r__3, r__4;

    /* Builtin functions */
    double sqrt(doublereal);

    /* Local variables */
    real c__;
    integer j;
    real s, v[3], s1, s2, t1, u1, u2, a11, a12, a21, a22, b11, b22, c12, c21;
    integer jc;
    real an, bn, cl, cq, cr;
    integer in;
    real u12, w11, w12, w21;
    integer jr;
    real 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;
    real c11r, c22r;
    logical ilq;
    real u12l, tau, sqi;
    logical ilz;
    real ulp, sqr, szi, szr, ad11l, ad12l, ad21l, ad22l, ad32l, wabs, atol, 
            btol, temp;
    extern /* Subroutine */ int srot_(integer *, real *, integer *, real *, 
            integer *, real *, real *), slag2_(real *, integer *, real *, 
            integer *, real *, real *, real *, real *, real *, real *);
    real temp2, s1inv, scale;
    extern logical lsame_(char *, char *);
    integer iiter, ilast, jiter;
    real anorm, bnorm;
    integer maxit;
    real tempi, tempr;
    logical ilazr2;
    extern doublereal slapy2_(real *, real *), slapy3_(real *, real *, real *)
            ;
    extern /* Subroutine */ int slasv2_(real *, real *, real *, real *, real *
, real *, real *, real *, real *);
    real ascale, bscale;
    extern doublereal slamch_(char *);
    real safmin;
    extern /* Subroutine */ int slarfg_(integer *, real *, real *, integer *, 
            real *);
    real safmax;
    extern /* Subroutine */ int xerbla_(char *, integer *);
    real eshift;
    logical ilschr;
    integer icompq, ilastm;
    extern doublereal slanhs_(char *, integer *, real *, integer *, real *);
    extern /* Subroutine */ int slartg_(real *, real *, real *, real *, real *
);
    integer ischur;
    extern /* Subroutine */ int slaset_(char *, integer *, integer *, real *, 
            real *, real *, integer *);
    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 */
/*  ======= */

/*  SHGEQZ 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 SGGHRD. */

/*  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 SGGHRD 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) REAL 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) REAL 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) REAL array, dimension (N) */
/*          The real parts of each scalar alpha defining an eigenvalue */
/*          of GNEP. */

/*  ALPHAI  (output) REAL 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) REAL 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) REAL 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) REAL 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) REAL 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] = (real) 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_("SHGEQZ", &i__1);
        return 0;
    } else if (lquery) {
        return 0;
    }

/*     Quick return if possible */

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

/*     Initialize Q and Z */

    if (icompq == 3) {
        slaset_("Full", n, n, &c_b12, &c_b13, &q[q_offset], ldq);
    }
    if (icompz == 3) {
        slaset_("Full", n, n, &c_b12, &c_b13, &z__[z_offset], ldz);
    }

/*     Machine Constants */

    in = *ihi + 1 - *ilo;
    safmin = slamch_("S");
    safmax = 1.f / safmin;
    ulp = slamch_("E") * slamch_("B");
    anorm = slanhs_("F", &in, &h__[*ilo + *ilo * h_dim1], ldh, &work[1]);
    bnorm = slanhs_("F", &in, &t[*ilo + *ilo * t_dim1], ldt, &work[1]);
/* Computing MAX */
    r__1 = safmin, r__2 = ulp * anorm;
    atol = dmax(r__1,r__2);
/* Computing MAX */
    r__1 = safmin, r__2 = ulp * bnorm;
    btol = dmax(r__1,r__2);
    ascale = 1.f / dmax(safmin,anorm);
    bscale = 1.f / dmax(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.f) {
            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.f;
        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.f;
    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 ((r__1 = h__[ilast + (ilast - 1) * h_dim1], dabs(r__1)) <= 
                    atol) {
                h__[ilast + (ilast - 1) * h_dim1] = 0.f;
                goto L80;
            }
        }

        if ((r__1 = t[ilast + ilast * t_dim1], dabs(r__1)) <= btol) {
            t[ilast + ilast * t_dim1] = 0.f;
            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 ((r__1 = h__[j + (j - 1) * h_dim1], dabs(r__1)) <= atol) {
                    h__[j + (j - 1) * h_dim1] = 0.f;
                    ilazro = TRUE_;
                } else {
                    ilazro = FALSE_;
                }
            }

/*           Test 2: for T(j,j)=0 */

            if ((r__1 = t[j + j * t_dim1], dabs(r__1)) < btol) {
                t[j + j * t_dim1] = 0.f;

/*              Test 1a: Check for 2 consecutive small subdiagonals in A */

                ilazr2 = FALSE_;
                if (! ilazro) {
                    temp = (r__1 = h__[j + (j - 1) * h_dim1], dabs(r__1));
                    temp2 = (r__1 = h__[j + j * h_dim1], dabs(r__1));
                    tempr = dmax(temp,temp2);
                    if (tempr < 1.f && tempr != 0.f) {
                        temp /= tempr;
                        temp2 /= tempr;
                    }
                    if (temp * (ascale * (r__1 = h__[j + 1 + j * h_dim1], 
                            dabs(r__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];
                        slartg_(&temp, &h__[jch + 1 + jch * h_dim1], &c__, &s, 
                                 &h__[jch + jch * h_dim1]);
                        h__[jch + 1 + jch * h_dim1] = 0.f;
                        i__4 = ilastm - jch;
                        srot_(&i__4, &h__[jch + (jch + 1) * h_dim1], ldh, &
                                h__[jch + 1 + (jch + 1) * h_dim1], ldh, &c__, 
                                &s);
                        i__4 = ilastm - jch;
                        srot_(&i__4, &t[jch + (jch + 1) * t_dim1], ldt, &t[
                                jch + 1 + (jch + 1) * t_dim1], ldt, &c__, &s);
                        if (ilq) {
                            srot_(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 ((r__1 = t[jch + 1 + (jch + 1) * t_dim1], dabs(
                                r__1)) >= btol) {
                            if (jch + 1 >= ilast) {
                                goto L80;
                            } else {
                                ifirst = jch + 1;
                                goto L110;
                            }
                        }
                        t[jch + 1 + (jch + 1) * t_dim1] = 0.f;
/* 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];
                        slartg_(&temp, &t[jch + 1 + (jch + 1) * t_dim1], &c__, 
                                 &s, &t[jch + (jch + 1) * t_dim1]);
                        t[jch + 1 + (jch + 1) * t_dim1] = 0.f;
                        if (jch < ilastm - 1) {
                            i__4 = ilastm - jch - 1;
                            srot_(&i__4, &t[jch + (jch + 2) * t_dim1], ldt, &
                                    t[jch + 1 + (jch + 2) * t_dim1], ldt, &
                                    c__, &s);
                        }
                        i__4 = ilastm - jch + 2;
                        srot_(&i__4, &h__[jch + (jch - 1) * h_dim1], ldh, &
                                h__[jch + 1 + (jch - 1) * h_dim1], ldh, &c__, 
                                &s);
                        if (ilq) {
                            srot_(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];
                        slartg_(&temp, &h__[jch + 1 + (jch - 1) * h_dim1], &
                                c__, &s, &h__[jch + 1 + jch * h_dim1]);
                        h__[jch + 1 + (jch - 1) * h_dim1] = 0.f;
                        i__4 = jch + 1 - ifrstm;
                        srot_(&i__4, &h__[ifrstm + jch * h_dim1], &c__1, &h__[
                                ifrstm + (jch - 1) * h_dim1], &c__1, &c__, &s)
                                ;
                        i__4 = jch - ifrstm;
                        srot_(&i__4, &t[ifrstm + jch * t_dim1], &c__1, &t[
                                ifrstm + (jch - 1) * t_dim1], &c__1, &c__, &s)
                                ;
                        if (ilz) {
                            srot_(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];
        slartg_(&temp, &h__[ilast + (ilast - 1) * h_dim1], &c__, &s, &h__[
                ilast + ilast * h_dim1]);
        h__[ilast + (ilast - 1) * h_dim1] = 0.f;
        i__2 = ilast - ifrstm;
        srot_(&i__2, &h__[ifrstm + ilast * h_dim1], &c__1, &h__[ifrstm + (
                ilast - 1) * h_dim1], &c__1, &c__, &s);
        i__2 = ilast - ifrstm;
        srot_(&i__2, &t[ifrstm + ilast * t_dim1], &c__1, &t[ifrstm + (ilast - 
                1) * t_dim1], &c__1, &c__, &s);
        if (ilz) {
            srot_(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.f) {
            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.f;
        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.f;
        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 ((real) maxit * safmin * (r__1 = h__[ilast - 1 + ilast * 
                    h_dim1], dabs(r__1)) < (r__2 = t[ilast - 1 + (ilast - 1) *
                     t_dim1], dabs(r__2))) {
                eshift += h__[ilast - 1 + ilast * h_dim1] / t[ilast - 1 + (
                        ilast - 1) * t_dim1];
            } else {
                eshift += 1.f / (safmin * (real) maxit);
            }
            s1 = 1.f;
            wr = eshift;

        } else {

/*           Shifts based on the generalized eigenvalues of the */
/*           bottom-right 2x2 block of A and B. The first eigenvalue */
/*           returned by SLAG2 is the Wilkinson shift (AEP p.512), */

            r__1 = safmin * 100.f;
            slag2_(&h__[ilast - 1 + (ilast - 1) * h_dim1], ldh, &t[ilast - 1 
                    + (ilast - 1) * t_dim1], ldt, &r__1, &s1, &s2, &wr, &wr2, 
                    &wi);

/* Computing MAX */
/* Computing MAX */
            r__3 = 1.f, r__4 = dabs(wr), r__3 = max(r__3,r__4), r__4 = dabs(
                    wi);
            r__1 = s1, r__2 = safmin * dmax(r__3,r__4);
            temp = dmax(r__1,r__2);
            if (wi != 0.f) {
                goto L200;
            }
        }

/*        Fiddle with shift to avoid overflow */

        temp = dmin(ascale,1.f) * (safmax * .5f);
        if (s1 > temp) {
            scale = temp / s1;
        } else {
            scale = 1.f;
        }

        temp = dmin(bscale,1.f) * (safmax * .5f);
        if (dabs(wr) > temp) {
/* Computing MIN */
            r__1 = scale, r__2 = temp / dabs(wr);
            scale = dmin(r__1,r__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 = (r__1 = s1 * h__[j + (j - 1) * h_dim1], dabs(r__1));
            temp2 = (r__1 = s1 * h__[j + j * h_dim1] - wr * t[j + j * t_dim1],
                     dabs(r__1));
            tempr = dmax(temp,temp2);
            if (tempr < 1.f && tempr != 0.f) {
                temp /= tempr;
                temp2 /= tempr;
            }
            if ((r__1 = ascale * h__[j + 1 + j * h_dim1] * temp, dabs(r__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];
        slartg_(&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];
                slartg_(&temp, &h__[j + 1 + (j - 1) * h_dim1], &c__, &s, &h__[
                        j + (j - 1) * h_dim1]);
                h__[j + 1 + (j - 1) * h_dim1] = 0.f;
            }

            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];
            slartg_(&temp, &t[j + 1 + j * t_dim1], &c__, &s, &t[j + 1 + (j + 
                    1) * t_dim1]);
            t[j + 1 + j * t_dim1] = 0.f;

/* 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 ) */

            slasv2_(&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.f) {
                cr = -cr;
                sr = -sr;
                b11 = -b11;
                b22 = -b22;
            }

            i__2 = ilastm + 1 - ifirst;
            srot_(&i__2, &h__[ilast - 1 + (ilast - 1) * h_dim1], ldh, &h__[
                    ilast + (ilast - 1) * h_dim1], ldh, &cl, &sl);
            i__2 = ilast + 1 - ifrstm;
            srot_(&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;
                srot_(&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;
                srot_(&i__2, &t[ifrstm + (ilast - 1) * t_dim1], &c__1, &t[
                        ifrstm + ilast * t_dim1], &c__1, &cr, &sr);
            }

            if (ilq) {
                srot_(n, &q[(ilast - 1) * q_dim1 + 1], &c__1, &q[ilast * 
                        q_dim1 + 1], &c__1, &cl, &sl);
            }
            if (ilz) {
                srot_(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.f;
            t[ilast + (ilast - 1) * t_dim1] = 0.f;
            t[ilast + ilast * t_dim1] = b22;

/*           If B22 is negative, negate column ILAST */

            if (b22 < 0.f) {
                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 */

            r__1 = safmin * 100.f;
            slag2_(&h__[ilast - 1 + (ilast - 1) * h_dim1], ldh, &t[ilast - 1 
                    + (ilast - 1) * t_dim1], ldt, &r__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.f) {
                goto L350;
            }
            s1inv = 1.f / 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 (dabs(c11r) + dabs(c11i) + dabs(c12) > dabs(c21) + dabs(c22r) 
                    + dabs(c22i)) {
                t1 = slapy3_(&c12, &c11r, &c11i);
                cz = c12 / t1;
                szr = -c11r / t1;
                szi = -c11i / t1;
            } else {
                cz = slapy2_(&c22r, &c22i);
                if (cz <= safmin) {
                    cz = 0.f;
                    szr = 1.f;
                    szi = 0.f;
                } else {
                    tempr = c22r / cz;
                    tempi = c22i / cz;
                    t1 = slapy2_(&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 = dabs(a11) + dabs(a12) + dabs(a21) + dabs(a22);
            bn = dabs(b11) + dabs(b22);
            wabs = dabs(wr) + dabs(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 = slapy2_(&a1r, &a1i);
                if (cq <= safmin) {
                    cq = 0.f;
                    sqr = 1.f;
                    sqi = 0.f;
                } else {
                    tempr = a1r / cq;
                    tempi = a1i / cq;
                    sqr = tempr * a2r + tempi * a2i;
                    sqi = tempi * a2r - tempr * a2i;
                }
            }
            t1 = slapy3_(&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 = slapy2_(&b1r, &b1i);
            b2r = cq * cz * b22 + tempr * b11;
            b2i = -tempi * b11;
            b2a = slapy2_(&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.f;
            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;

            slarfg_(&c__3, v, &v[1], &c__1, &tau);
            v[0] = 1.f;

/*           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];

                    slarfg_(&c__3, &h__[j + (j - 1) * h_dim1], &v[1], &c__1, &
                            tau);
                    v[0] = 1.f;
                    h__[j + 1 + (j - 1) * h_dim1] = 0.f;
                    h__[j + 2 + (j - 1) * h_dim1] = 0.f;
                }

                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 SLAGBC for details) */

/*              Swap rows to pivot */

                ilpivt = FALSE_;
/* Computing MAX */
                r__3 = (r__1 = t[j + 1 + (j + 1) * t_dim1], dabs(r__1)), r__4 
                        = (r__2 = t[j + 1 + (j + 2) * t_dim1], dabs(r__2));
                temp = dmax(r__3,r__4);
/* Computing MAX */
                r__3 = (r__1 = t[j + 2 + (j + 1) * t_dim1], dabs(r__1)), r__4 
                        = (r__2 = t[j + 2 + (j + 2) * t_dim1], dabs(r__2));
                temp2 = dmax(r__3,r__4);
                if (dmax(temp,temp2) < safmin) {
                    scale = 0.f;
                    u1 = 1.f;
                    u2 = 0.f;
                    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 (dabs(w12) > dabs(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.f;

/*              Compute SCALE */

                scale = 1.f;
                if (dabs(w22) < safmin) {
                    scale = 0.f;
                    u2 = 1.f;
                    u1 = -w12 / w11;
                    goto L250;
                }
                if (dabs(w22) < dabs(u2)) {
                    scale = (r__1 = w22 / u2, dabs(r__1));
                }
                if (dabs(w11) < dabs(u1)) {
/* Computing MIN */
                    r__2 = scale, r__3 = (r__1 = w11 / u1, dabs(r__1));
                    scale = dmin(r__2,r__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 */
                r__1 = scale;
/* Computing 2nd power */
                r__2 = u1;
/* Computing 2nd power */
                r__3 = u2;
                t1 = sqrt(r__1 * r__1 + r__2 * r__2 + r__3 * r__3);
                tau = scale / t1 + 1.f;
                vs = -1.f / (scale + t1);
                v[0] = 1.f;
                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.f;
                t[j + 2 + j * t_dim1] = 0.f;
/* L290: */
            }

/*           Last elements: Use Givens rotations */

/*           Rotations from the left */

            j = ilast - 1;
            temp = h__[j + (j - 1) * h_dim1];
            slartg_(&temp, &h__[j + 1 + (j - 1) * h_dim1], &c__, &s, &h__[j + 
                    (j - 1) * h_dim1]);
            h__[j + 1 + (j - 1) * h_dim1] = 0.f;

            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];
            slartg_(&temp, &t[j + 1 + j * t_dim1], &c__, &s, &t[j + 1 + (j + 
                    1) * t_dim1]);
            t[j + 1 + j * t_dim1] = 0.f;

            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.f) {
            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.f;
        beta[j] = t[j + j * t_dim1];
/* L410: */
    }

/*     Normal Termination */

    *info = 0;

/*     Exit (other than argument error) -- return optimal workspace size */

L420:
    work[1] = (real) (*n);
    return 0;

/*     End of SHGEQZ */

} /* shgeqz_ */