#include "blaswrap.h"
#include "f2c.h"

/* Subroutine */ int stgsen_(integer *ijob, logical *wantq, logical *wantz, 
	logical *select, integer *n, real *a, integer *lda, real *b, integer *
	ldb, real *alphar, real *alphai, real *beta, real *q, integer *ldq, 
	real *z__, integer *ldz, integer *m, real *pl, real *pr, real *dif, 
	real *work, integer *lwork, integer *iwork, integer *liwork, integer *
	info)
{
/*  -- LAPACK routine (version 3.0) --   
       Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,   
       Courant Institute, Argonne National Lab, and Rice University   
       June 30, 1999   


    Purpose   
    =======   

    STGSEN reorders the generalized real Schur decomposition of a real   
    matrix pair (A, B) (in terms of an orthonormal equivalence trans-   
    formation Q' * (A, B) * Z), so that a selected cluster of eigenvalues   
    appears in the leading diagonal blocks of the upper quasi-triangular   
    matrix A and the upper triangular B. The leading columns of Q and   
    Z form orthonormal bases of the corresponding left and right eigen-   
    spaces (deflating subspaces). (A, B) must be in generalized real   
    Schur canonical form (as returned by SGGES), i.e. A is block upper   
    triangular with 1-by-1 and 2-by-2 diagonal blocks. B is upper   
    triangular.   

    STGSEN also computes the generalized eigenvalues   

                w(j) = (ALPHAR(j) + i*ALPHAI(j))/BETA(j)   

    of the reordered matrix pair (A, B).   

    Optionally, STGSEN computes the estimates of reciprocal condition   
    numbers for eigenvalues and eigenspaces. These are Difu[(A11,B11),   
    (A22,B22)] and Difl[(A11,B11), (A22,B22)], i.e. the separation(s)   
    between the matrix pairs (A11, B11) and (A22,B22) that correspond to   
    the selected cluster and the eigenvalues outside the cluster, resp.,   
    and norms of "projections" onto left and right eigenspaces w.r.t.   
    the selected cluster in the (1,1)-block.   

    Arguments   
    =========   

    IJOB    (input) INTEGER   
            Specifies whether condition numbers are required for the   
            cluster of eigenvalues (PL and PR) or the deflating subspaces   
            (Difu and Difl):   
             =0: Only reorder w.r.t. SELECT. No extras.   
             =1: Reciprocal of norms of "projections" onto left and right   
                 eigenspaces w.r.t. the selected cluster (PL and PR).   
             =2: Upper bounds on Difu and Difl. F-norm-based estimate   
                 (DIF(1:2)).   
             =3: Estimate of Difu and Difl. 1-norm-based estimate   
                 (DIF(1:2)).   
                 About 5 times as expensive as IJOB = 2.   
             =4: Compute PL, PR and DIF (i.e. 0, 1 and 2 above): Economic   
                 version to get it all.   
             =5: Compute PL, PR and DIF (i.e. 0, 1 and 3 above)   

    WANTQ   (input) LOGICAL   
            .TRUE. : update the left transformation matrix Q;   
            .FALSE.: do not update Q.   

    WANTZ   (input) LOGICAL   
            .TRUE. : update the right transformation matrix Z;   
            .FALSE.: do not update Z.   

    SELECT  (input) LOGICAL array, dimension (N)   
            SELECT specifies the eigenvalues in the selected cluster.   
            To select a real eigenvalue w(j), SELECT(j) must be set to   
            .TRUE.. To select a complex conjugate pair of eigenvalues   
            w(j) and w(j+1), corresponding to a 2-by-2 diagonal block,   
            either SELECT(j) or SELECT(j+1) or both must be set to   
            .TRUE.; a complex conjugate pair of eigenvalues must be   
            either both included in the cluster or both excluded.   

    N       (input) INTEGER   
            The order of the matrices A and B. N >= 0.   

    A       (input/output) REAL array, dimension(LDA,N)   
            On entry, the upper quasi-triangular matrix A, with (A, B) in   
            generalized real Schur canonical form.   
            On exit, A is overwritten by the reordered matrix A.   

    LDA     (input) INTEGER   
            The leading dimension of the array A. LDA >= max(1,N).   

    B       (input/output) REAL array, dimension(LDB,N)   
            On entry, the upper triangular matrix B, with (A, B) in   
            generalized real Schur canonical form.   
            On exit, B is overwritten by the reordered matrix B.   

    LDB     (input) INTEGER   
            The leading dimension of the array B. LDB >= max(1,N).   

    ALPHAR  (output) REAL array, dimension (N)   
    ALPHAI  (output) REAL array, dimension (N)   
    BETA    (output) REAL array, dimension (N)   
            On exit, (ALPHAR(j) + ALPHAI(j)*i)/BETA(j), j=1,...,N, will   
            be the generalized eigenvalues.  ALPHAR(j) + ALPHAI(j)*i   
            and BETA(j),j=1,...,N  are the diagonals of the complex Schur   
            form (S,T) that would result if the 2-by-2 diagonal blocks of   
            the real generalized Schur form of (A,B) were further reduced   
            to triangular form using complex unitary transformations.   
            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) negative.   

    Q       (input/output) REAL array, dimension (LDQ,N)   
            On entry, if WANTQ = .TRUE., Q is an N-by-N matrix.   
            On exit, Q has been postmultiplied by the left orthogonal   
            transformation matrix which reorder (A, B); The leading M   
            columns of Q form orthonormal bases for the specified pair of   
            left eigenspaces (deflating subspaces).   
            If WANTQ = .FALSE., Q is not referenced.   

    LDQ     (input) INTEGER   
            The leading dimension of the array Q.  LDQ >= 1;   
            and if WANTQ = .TRUE., LDQ >= N.   

    Z       (input/output) REAL array, dimension (LDZ,N)   
            On entry, if WANTZ = .TRUE., Z is an N-by-N matrix.   
            On exit, Z has been postmultiplied by the left orthogonal   
            transformation matrix which reorder (A, B); The leading M   
            columns of Z form orthonormal bases for the specified pair of   
            left eigenspaces (deflating subspaces).   
            If WANTZ = .FALSE., Z is not referenced.   

    LDZ     (input) INTEGER   
            The leading dimension of the array Z. LDZ >= 1;   
            If WANTZ = .TRUE., LDZ >= N.   

    M       (output) INTEGER   
            The dimension of the specified pair of left and right eigen-   
            spaces (deflating subspaces). 0 <= M <= N.   

    PL, PR  (output) REAL   
            If IJOB = 1, 4 or 5, PL, PR are lower bounds on the   
            reciprocal of the norm of "projections" onto left and right   
            eigenspaces with respect to the selected cluster.   
            0 < PL, PR <= 1.   
            If M = 0 or M = N, PL = PR  = 1.   
            If IJOB = 0, 2 or 3, PL and PR are not referenced.   

    DIF     (output) REAL array, dimension (2).   
            If IJOB >= 2, DIF(1:2) store the estimates of Difu and Difl.   
            If IJOB = 2 or 4, DIF(1:2) are F-norm-based upper bounds on   
            Difu and Difl. If IJOB = 3 or 5, DIF(1:2) are 1-norm-based   
            estimates of Difu and Difl.   
            If M = 0 or N, DIF(1:2) = F-norm([A, B]).   
            If IJOB = 0 or 1, DIF is not referenced.   

    WORK    (workspace/output) REAL array, dimension (LWORK)   
            IF IJOB = 0, WORK is not referenced.  Otherwise,   
            on exit, if INFO = 0, WORK(1) returns the optimal LWORK.   

    LWORK   (input) INTEGER   
            The dimension of the array WORK. LWORK >=  4*N+16.   
            If IJOB = 1, 2 or 4, LWORK >= MAX(4*N+16, 2*M*(N-M)).   
            If IJOB = 3 or 5, LWORK >= MAX(4*N+16, 4*M*(N-M)).   

            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.   

    IWORK   (workspace/output) INTEGER array, dimension (LIWORK)   
            IF IJOB = 0, IWORK is not referenced.  Otherwise,   
            on exit, if INFO = 0, IWORK(1) returns the optimal LIWORK.   

    LIWORK  (input) INTEGER   
            The dimension of the array IWORK. LIWORK >= 1.   
            If IJOB = 1, 2 or 4, LIWORK >=  N+6.   
            If IJOB = 3 or 5, LIWORK >= MAX(2*M*(N-M), N+6).   

            If LIWORK = -1, then a workspace query is assumed; the   
            routine only calculates the optimal size of the IWORK array,   
            returns this value as the first entry of the IWORK array, and   
            no error message related to LIWORK is issued by XERBLA.   

    INFO    (output) INTEGER   
              =0: Successful exit.   
              <0: If INFO = -i, the i-th argument had an illegal value.   
              =1: Reordering of (A, B) failed because the transformed   
                  matrix pair (A, B) would be too far from generalized   
                  Schur form; the problem is very ill-conditioned.   
                  (A, B) may have been partially reordered.   
                  If requested, 0 is returned in DIF(*), PL and PR.   

    Further Details   
    ===============   

    STGSEN first collects the selected eigenvalues by computing   
    orthogonal U and W that move them to the top left corner of (A, B).   
    In other words, the selected eigenvalues are the eigenvalues of   
    (A11, B11) in:   

                  U'*(A, B)*W = (A11 A12) (B11 B12) n1   
                                ( 0  A22),( 0  B22) n2   
                                  n1  n2    n1  n2   

    where N = n1+n2 and U' means the transpose of U. The first n1 columns   
    of U and W span the specified pair of left and right eigenspaces   
    (deflating subspaces) of (A, B).   

    If (A, B) has been obtained from the generalized real Schur   
    decomposition of a matrix pair (C, D) = Q*(A, B)*Z', then the   
    reordered generalized real Schur form of (C, D) is given by   

             (C, D) = (Q*U)*(U'*(A, B)*W)*(Z*W)',   

    and the first n1 columns of Q*U and Z*W span the corresponding   
    deflating subspaces of (C, D) (Q and Z store Q*U and Z*W, resp.).   

    Note that if the selected eigenvalue is sufficiently ill-conditioned,   
    then its value may differ significantly from its value before   
    reordering.   

    The reciprocal condition numbers of the left and right eigenspaces   
    spanned by the first n1 columns of U and W (or Q*U and Z*W) may   
    be returned in DIF(1:2), corresponding to Difu and Difl, resp.   

    The Difu and Difl are defined as:   

         Difu[(A11, B11), (A22, B22)] = sigma-min( Zu )   
    and   
         Difl[(A11, B11), (A22, B22)] = Difu[(A22, B22), (A11, B11)],   

    where sigma-min(Zu) is the smallest singular value of the   
    (2*n1*n2)-by-(2*n1*n2) matrix   

         Zu = [ kron(In2, A11)  -kron(A22', In1) ]   
              [ kron(In2, B11)  -kron(B22', In1) ].   

    Here, Inx is the identity matrix of size nx and A22' is the   
    transpose of A22. kron(X, Y) is the Kronecker product between   
    the matrices X and Y.   

    When DIF(2) is small, small changes in (A, B) can cause large changes   
    in the deflating subspace. An approximate (asymptotic) bound on the   
    maximum angular error in the computed deflating subspaces is   

         EPS * norm((A, B)) / DIF(2),   

    where EPS is the machine precision.   

    The reciprocal norm of the projectors on the left and right   
    eigenspaces associated with (A11, B11) may be returned in PL and PR.   
    They are computed as follows. First we compute L and R so that   
    P*(A, B)*Q is block diagonal, where   

         P = ( I -L ) n1           Q = ( I R ) n1   
             ( 0  I ) n2    and        ( 0 I ) n2   
               n1 n2                    n1 n2   

    and (L, R) is the solution to the generalized Sylvester equation   

         A11*R - L*A22 = -A12   
         B11*R - L*B22 = -B12   

    Then PL = (F-norm(L)**2+1)**(-1/2) and PR = (F-norm(R)**2+1)**(-1/2).   
    An approximate (asymptotic) bound on the average absolute error of   
    the selected eigenvalues is   

         EPS * norm((A, B)) / PL.   

    There are also global error bounds which valid for perturbations up   
    to a certain restriction:  A lower bound (x) on the smallest   
    F-norm(E,F) for which an eigenvalue of (A11, B11) may move and   
    coalesce with an eigenvalue of (A22, B22) under perturbation (E,F),   
    (i.e. (A + E, B + F), is   

     x = min(Difu,Difl)/((1/(PL*PL)+1/(PR*PR))**(1/2)+2*max(1/PL,1/PR)).   

    An approximate bound on x can be computed from DIF(1:2), PL and PR.   

    If y = ( F-norm(E,F) / x) <= 1, the angles between the perturbed   
    (L', R') and unperturbed (L, R) left and right deflating subspaces   
    associated with the selected cluster in the (1,1)-blocks can be   
    bounded as   

     max-angle(L, L') <= arctan( y * PL / (1 - y * (1 - PL * PL)**(1/2))   
     max-angle(R, R') <= arctan( y * PR / (1 - y * (1 - PR * PR)**(1/2))   

    See LAPACK User's Guide section 4.11 or the following references   
    for more information.   

    Note that if the default method for computing the Frobenius-norm-   
    based estimate DIF is not wanted (see SLATDF), then the parameter   
    IDIFJB (see below) should be changed from 3 to 4 (routine SLATDF   
    (IJOB = 2 will be used)). See STGSYL for more details.   

    Based on contributions by   
       Bo Kagstrom and Peter Poromaa, Department of Computing Science,   
       Umea University, S-901 87 Umea, Sweden.   

    References   
    ==========   

    [1] B. Kagstrom; A Direct Method for Reordering Eigenvalues in the   
        Generalized Real Schur Form of a Regular Matrix Pair (A, B), in   
        M.S. Moonen et al (eds), Linear Algebra for Large Scale and   
        Real-Time Applications, Kluwer Academic Publ. 1993, pp 195-218.   

    [2] B. Kagstrom and P. Poromaa; Computing Eigenspaces with Specified   
        Eigenvalues of a Regular Matrix Pair (A, B) and Condition   
        Estimation: Theory, Algorithms and Software,   
        Report UMINF - 94.04, Department of Computing Science, Umea   
        University, S-901 87 Umea, Sweden, 1994. Also as LAPACK Working   
        Note 87. To appear in Numerical Algorithms, 1996.   

    [3] B. Kagstrom and P. Poromaa, LAPACK-Style Algorithms and Software   
        for Solving the Generalized Sylvester Equation and Estimating the   
        Separation between Regular Matrix Pairs, Report UMINF - 93.23,   
        Department of Computing Science, Umea University, S-901 87 Umea,   
        Sweden, December 1993, Revised April 1994, Also as LAPACK Working   
        Note 75. To appear in ACM Trans. on Math. Software, Vol 22, No 1,   
        1996.   

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


       Decode and test the input parameters   

       Parameter adjustments */
    /* Table of constant values */
    static integer c__1 = 1;
    static integer c__2 = 2;
    static real c_b28 = 1.f;
    
    /* System generated locals */
    integer a_dim1, a_offset, b_dim1, b_offset, q_dim1, q_offset, z_dim1, 
	    z_offset, i__1, i__2;
    real r__1;
    /* Builtin functions */
    double sqrt(doublereal), r_sign(real *, real *);
    /* Local variables */
    static integer kase;
    static logical pair;
    static integer ierr;
    static real dsum;
    static logical swap;
    extern /* Subroutine */ int slag2_(real *, integer *, real *, integer *, 
	    real *, real *, real *, real *, real *, real *);
    static integer i__, k;
    static logical wantd;
    static integer lwmin;
    static logical wantp;
    static integer n1, n2;
    static logical wantd1, wantd2;
    static integer kk;
    static real dscale;
    static integer ks;
    static real rdscal;
    extern doublereal slamch_(char *);
    extern /* Subroutine */ int xerbla_(char *, integer *), slacon_(
	    integer *, real *, real *, integer *, real *, integer *), slacpy_(
	    char *, integer *, integer *, real *, integer *, real *, integer *
	    ), stgexc_(logical *, logical *, integer *, real *, 
	    integer *, real *, integer *, real *, integer *, real *, integer *
	    , integer *, integer *, real *, integer *, integer *);
    static integer liwmin;
    extern /* Subroutine */ int slassq_(integer *, real *, integer *, real *, 
	    real *);
    static real smlnum;
    static integer mn2;
    static logical lquery;
    extern /* Subroutine */ int stgsyl_(char *, integer *, integer *, integer 
	    *, real *, integer *, real *, integer *, real *, integer *, real *
	    , integer *, real *, integer *, real *, integer *, real *, real *,
	     real *, integer *, integer *, integer *);
    static integer ijb;
    static real eps;
#define a_ref(a_1,a_2) a[(a_2)*a_dim1 + a_1]
#define b_ref(a_1,a_2) b[(a_2)*b_dim1 + a_1]
#define q_ref(a_1,a_2) q[(a_2)*q_dim1 + a_1]


    --select;
    a_dim1 = *lda;
    a_offset = 1 + a_dim1 * 1;
    a -= a_offset;
    b_dim1 = *ldb;
    b_offset = 1 + b_dim1 * 1;
    b -= b_offset;
    --alphar;
    --alphai;
    --beta;
    q_dim1 = *ldq;
    q_offset = 1 + q_dim1 * 1;
    q -= q_offset;
    z_dim1 = *ldz;
    z_offset = 1 + z_dim1 * 1;
    z__ -= z_offset;
    --dif;
    --work;
    --iwork;

    /* Function Body */
    *info = 0;
    lquery = *lwork == -1 || *liwork == -1;

    if (*ijob < 0 || *ijob > 5) {
	*info = -1;
    } else if (*n < 0) {
	*info = -5;
    } else if (*lda < max(1,*n)) {
	*info = -7;
    } else if (*ldb < max(1,*n)) {
	*info = -9;
    } else if (*ldq < 1 || *wantq && *ldq < *n) {
	*info = -14;
    } else if (*ldz < 1 || *wantz && *ldz < *n) {
	*info = -16;
    }

    if (*info != 0) {
	i__1 = -(*info);
	xerbla_("STGSEN", &i__1);
	return 0;
    }

/*     Get machine constants */

    eps = slamch_("P");
    smlnum = slamch_("S") / eps;
    ierr = 0;

    wantp = *ijob == 1 || *ijob >= 4;
    wantd1 = *ijob == 2 || *ijob == 4;
    wantd2 = *ijob == 3 || *ijob == 5;
    wantd = wantd1 || wantd2;

/*     Set M to the dimension of the specified pair of deflating   
       subspaces. */

    *m = 0;
    pair = FALSE_;
    i__1 = *n;
    for (k = 1; k <= i__1; ++k) {
	if (pair) {
	    pair = FALSE_;
	} else {
	    if (k < *n) {
		if (a_ref(k + 1, k) == 0.f) {
		    if (select[k]) {
			++(*m);
		    }
		} else {
		    pair = TRUE_;
		    if (select[k] || select[k + 1]) {
			*m += 2;
		    }
		}
	    } else {
		if (select[*n]) {
		    ++(*m);
		}
	    }
	}
/* L10: */
    }

    if (*ijob == 1 || *ijob == 2 || *ijob == 4) {
/* Computing MAX */
	i__1 = 1, i__2 = (*n << 2) + 16, i__1 = max(i__1,i__2), i__2 = (*m << 
		1) * (*n - *m);
	lwmin = max(i__1,i__2);
/* Computing MAX */
	i__1 = 1, i__2 = *n + 6;
	liwmin = max(i__1,i__2);
    } else if (*ijob == 3 || *ijob == 5) {
/* Computing MAX */
	i__1 = 1, i__2 = (*n << 2) + 16, i__1 = max(i__1,i__2), i__2 = (*m << 
		2) * (*n - *m);
	lwmin = max(i__1,i__2);
/* Computing MAX */
	i__1 = 1, i__2 = (*m << 1) * (*n - *m), i__1 = max(i__1,i__2), i__2 = 
		*n + 6;
	liwmin = max(i__1,i__2);
    } else {
/* Computing MAX */
	i__1 = 1, i__2 = (*n << 2) + 16;
	lwmin = max(i__1,i__2);
	liwmin = 1;
    }

    work[1] = (real) lwmin;
    iwork[1] = liwmin;

    if (*lwork < lwmin && ! lquery) {
	*info = -22;
    } else if (*liwork < liwmin && ! lquery) {
	*info = -24;
    }

    if (*info != 0) {
	i__1 = -(*info);
	xerbla_("STGSEN", &i__1);
	return 0;
    } else if (lquery) {
	return 0;
    }

/*     Quick return if possible. */

    if (*m == *n || *m == 0) {
	if (wantp) {
	    *pl = 1.f;
	    *pr = 1.f;
	}
	if (wantd) {
	    dscale = 0.f;
	    dsum = 1.f;
	    i__1 = *n;
	    for (i__ = 1; i__ <= i__1; ++i__) {
		slassq_(n, &a_ref(1, i__), &c__1, &dscale, &dsum);
		slassq_(n, &b_ref(1, i__), &c__1, &dscale, &dsum);
/* L20: */
	    }
	    dif[1] = dscale * sqrt(dsum);
	    dif[2] = dif[1];
	}
	goto L60;
    }

/*     Collect the selected blocks at the top-left corner of (A, B). */

    ks = 0;
    pair = FALSE_;
    i__1 = *n;
    for (k = 1; k <= i__1; ++k) {
	if (pair) {
	    pair = FALSE_;
	} else {

	    swap = select[k];
	    if (k < *n) {
		if (a_ref(k + 1, k) != 0.f) {
		    pair = TRUE_;
		    swap = swap || select[k + 1];
		}
	    }

	    if (swap) {
		++ks;

/*              Swap the K-th block to position KS.   
                Perform the reordering of diagonal blocks in (A, B)   
                by orthogonal transformation matrices and update   
                Q and Z accordingly (if requested): */

		kk = k;
		if (k != ks) {
		    stgexc_(wantq, wantz, n, &a[a_offset], lda, &b[b_offset], 
			    ldb, &q[q_offset], ldq, &z__[z_offset], ldz, &kk, 
			    &ks, &work[1], lwork, &ierr);
		}

		if (ierr > 0) {

/*                 Swap is rejected: exit. */

		    *info = 1;
		    if (wantp) {
			*pl = 0.f;
			*pr = 0.f;
		    }
		    if (wantd) {
			dif[1] = 0.f;
			dif[2] = 0.f;
		    }
		    goto L60;
		}

		if (pair) {
		    ++ks;
		}
	    }
	}
/* L30: */
    }
    if (wantp) {

/*        Solve generalized Sylvester equation for R and L   
          and compute PL and PR. */

	n1 = *m;
	n2 = *n - *m;
	i__ = n1 + 1;
	ijb = 0;
	slacpy_("Full", &n1, &n2, &a_ref(1, i__), lda, &work[1], &n1);
	slacpy_("Full", &n1, &n2, &b_ref(1, i__), ldb, &work[n1 * n2 + 1], &
		n1);
	i__1 = *lwork - (n1 << 1) * n2;
	stgsyl_("N", &ijb, &n1, &n2, &a[a_offset], lda, &a_ref(i__, i__), lda,
		 &work[1], &n1, &b[b_offset], ldb, &b_ref(i__, i__), ldb, &
		work[n1 * n2 + 1], &n1, &dscale, &dif[1], &work[(n1 * n2 << 1)
		 + 1], &i__1, &iwork[1], &ierr);

/*        Estimate the reciprocal of norms of "projections" onto left   
          and right eigenspaces. */

	rdscal = 0.f;
	dsum = 1.f;
	i__1 = n1 * n2;
	slassq_(&i__1, &work[1], &c__1, &rdscal, &dsum);
	*pl = rdscal * sqrt(dsum);
	if (*pl == 0.f) {
	    *pl = 1.f;
	} else {
	    *pl = dscale / (sqrt(dscale * dscale / *pl + *pl) * sqrt(*pl));
	}
	rdscal = 0.f;
	dsum = 1.f;
	i__1 = n1 * n2;
	slassq_(&i__1, &work[n1 * n2 + 1], &c__1, &rdscal, &dsum);
	*pr = rdscal * sqrt(dsum);
	if (*pr == 0.f) {
	    *pr = 1.f;
	} else {
	    *pr = dscale / (sqrt(dscale * dscale / *pr + *pr) * sqrt(*pr));
	}
    }

    if (wantd) {

/*        Compute estimates of Difu and Difl. */

	if (wantd1) {
	    n1 = *m;
	    n2 = *n - *m;
	    i__ = n1 + 1;
	    ijb = 3;

/*           Frobenius norm-based Difu-estimate. */

	    i__1 = *lwork - (n1 << 1) * n2;
	    stgsyl_("N", &ijb, &n1, &n2, &a[a_offset], lda, &a_ref(i__, i__), 
		    lda, &work[1], &n1, &b[b_offset], ldb, &b_ref(i__, i__), 
		    ldb, &work[n1 * n2 + 1], &n1, &dscale, &dif[1], &work[(n1 
		    << 1) * n2 + 1], &i__1, &iwork[1], &ierr);

/*           Frobenius norm-based Difl-estimate. */

	    i__1 = *lwork - (n1 << 1) * n2;
	    stgsyl_("N", &ijb, &n2, &n1, &a_ref(i__, i__), lda, &a[a_offset], 
		    lda, &work[1], &n2, &b_ref(i__, i__), ldb, &b[b_offset], 
		    ldb, &work[n1 * n2 + 1], &n2, &dscale, &dif[2], &work[(n1 
		    << 1) * n2 + 1], &i__1, &iwork[1], &ierr);
	} else {


/*           Compute 1-norm-based estimates of Difu and Difl using   
             reversed communication with SLACON. In each step a   
             generalized Sylvester equation or a transposed variant   
             is solved. */

	    kase = 0;
	    n1 = *m;
	    n2 = *n - *m;
	    i__ = n1 + 1;
	    ijb = 0;
	    mn2 = (n1 << 1) * n2;

/*           1-norm-based estimate of Difu. */

L40:
	    slacon_(&mn2, &work[mn2 + 1], &work[1], &iwork[1], &dif[1], &kase)
		    ;
	    if (kase != 0) {
		if (kase == 1) {

/*                 Solve generalized Sylvester equation. */

		    i__1 = *lwork - (n1 << 1) * n2;
		    stgsyl_("N", &ijb, &n1, &n2, &a[a_offset], lda, &a_ref(
			    i__, i__), lda, &work[1], &n1, &b[b_offset], ldb, 
			    &b_ref(i__, i__), ldb, &work[n1 * n2 + 1], &n1, &
			    dscale, &dif[1], &work[(n1 << 1) * n2 + 1], &i__1,
			     &iwork[1], &ierr);
		} else {

/*                 Solve the transposed variant. */

		    i__1 = *lwork - (n1 << 1) * n2;
		    stgsyl_("T", &ijb, &n1, &n2, &a[a_offset], lda, &a_ref(
			    i__, i__), lda, &work[1], &n1, &b[b_offset], ldb, 
			    &b_ref(i__, i__), ldb, &work[n1 * n2 + 1], &n1, &
			    dscale, &dif[1], &work[(n1 << 1) * n2 + 1], &i__1,
			     &iwork[1], &ierr);
		}
		goto L40;
	    }
	    dif[1] = dscale / dif[1];

/*           1-norm-based estimate of Difl. */

L50:
	    slacon_(&mn2, &work[mn2 + 1], &work[1], &iwork[1], &dif[2], &kase)
		    ;
	    if (kase != 0) {
		if (kase == 1) {

/*                 Solve generalized Sylvester equation. */

		    i__1 = *lwork - (n1 << 1) * n2;
		    stgsyl_("N", &ijb, &n2, &n1, &a_ref(i__, i__), lda, &a[
			    a_offset], lda, &work[1], &n2, &b_ref(i__, i__), 
			    ldb, &b[b_offset], ldb, &work[n1 * n2 + 1], &n2, &
			    dscale, &dif[2], &work[(n1 << 1) * n2 + 1], &i__1,
			     &iwork[1], &ierr);
		} else {

/*                 Solve the transposed variant. */

		    i__1 = *lwork - (n1 << 1) * n2;
		    stgsyl_("T", &ijb, &n2, &n1, &a_ref(i__, i__), lda, &a[
			    a_offset], lda, &work[1], &n2, &b_ref(i__, i__), 
			    ldb, &b[b_offset], ldb, &work[n1 * n2 + 1], &n2, &
			    dscale, &dif[2], &work[(n1 << 1) * n2 + 1], &i__1,
			     &iwork[1], &ierr);
		}
		goto L50;
	    }
	    dif[2] = dscale / dif[2];

	}
    }

L60:

/*     Compute generalized eigenvalues of reordered pair (A, B) and   
       normalize the generalized Schur form. */

    pair = FALSE_;
    i__1 = *n;
    for (k = 1; k <= i__1; ++k) {
	if (pair) {
	    pair = FALSE_;
	} else {

	    if (k < *n) {
		if (a_ref(k + 1, k) != 0.f) {
		    pair = TRUE_;
		}
	    }

	    if (pair) {

/*             Compute the eigenvalue(s) at position K. */

		work[1] = a_ref(k, k);
		work[2] = a_ref(k + 1, k);
		work[3] = a_ref(k, k + 1);
		work[4] = a_ref(k + 1, k + 1);
		work[5] = b_ref(k, k);
		work[6] = b_ref(k + 1, k);
		work[7] = b_ref(k, k + 1);
		work[8] = b_ref(k + 1, k + 1);
		r__1 = smlnum * eps;
		slag2_(&work[1], &c__2, &work[5], &c__2, &r__1, &beta[k], &
			beta[k + 1], &alphar[k], &alphar[k + 1], &alphai[k]);
		alphai[k + 1] = -alphai[k];

	    } else {

		if (r_sign(&c_b28, &b_ref(k, k)) < 0.f) {

/*                 If B(K,K) is negative, make it positive */

		    i__2 = *n;
		    for (i__ = 1; i__ <= i__2; ++i__) {
			a_ref(k, i__) = -a_ref(k, i__);
			b_ref(k, i__) = -b_ref(k, i__);
			q_ref(i__, k) = -q_ref(i__, k);
/* L80: */
		    }
		}

		alphar[k] = a_ref(k, k);
		alphai[k] = 0.f;
		beta[k] = b_ref(k, k);

	    }
	}
/* L70: */
    }

    work[1] = (real) lwmin;
    iwork[1] = liwmin;

    return 0;

/*     End of STGSEN */

} /* stgsen_ */

#undef q_ref
#undef b_ref
#undef a_ref


