dggesx.c

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/* dggesx.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 integer c__1 = 1;
static integer c__0 = 0;
static integer c_n1 = -1;
static doublereal c_b42 = 0.;
static doublereal c_b43 = 1.;

/* Subroutine */ int dggesx_(char *jobvsl, char *jobvsr, char *sort, L_fp 
        selctg, char *sense, integer *n, doublereal *a, integer *lda, 
        doublereal *b, integer *ldb, integer *sdim, doublereal *alphar, 
        doublereal *alphai, doublereal *beta, doublereal *vsl, integer *ldvsl, 
         doublereal *vsr, integer *ldvsr, doublereal *rconde, doublereal *
        rcondv, doublereal *work, integer *lwork, integer *iwork, integer *
        liwork, logical *bwork, integer *info)
{
    /* System generated locals */
    integer a_dim1, a_offset, b_dim1, b_offset, vsl_dim1, vsl_offset, 
            vsr_dim1, vsr_offset, i__1, i__2;
    doublereal d__1;

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

    /* Local variables */
    integer i__, ip;
    doublereal pl, pr, dif[2];
    integer ihi, ilo;
    doublereal eps;
    integer ijob;
    doublereal anrm, bnrm;
    integer ierr, itau, iwrk, lwrk;
    extern logical lsame_(char *, char *);
    integer ileft, icols;
    logical cursl, ilvsl, ilvsr;
    integer irows;
    extern /* Subroutine */ int dlabad_(doublereal *, doublereal *), dggbak_(
            char *, char *, integer *, integer *, integer *, doublereal *, 
            doublereal *, integer *, doublereal *, integer *, integer *), dggbal_(char *, integer *, doublereal *, integer 
            *, doublereal *, integer *, integer *, integer *, doublereal *, 
            doublereal *, doublereal *, integer *);
    logical lst2sl;
    extern doublereal dlamch_(char *), dlange_(char *, integer *, 
            integer *, doublereal *, integer *, doublereal *);
    extern /* Subroutine */ int dgghrd_(char *, char *, integer *, integer *, 
            integer *, doublereal *, integer *, doublereal *, integer *, 
            doublereal *, integer *, doublereal *, integer *, integer *), dlascl_(char *, integer *, integer *, doublereal 
            *, doublereal *, integer *, integer *, doublereal *, integer *, 
            integer *);
    logical ilascl, ilbscl;
    extern /* Subroutine */ int dgeqrf_(integer *, integer *, doublereal *, 
            integer *, doublereal *, doublereal *, integer *, integer *), 
            dlacpy_(char *, integer *, integer *, doublereal *, integer *, 
            doublereal *, integer *);
    doublereal safmin;
    extern /* Subroutine */ int dlaset_(char *, integer *, integer *, 
            doublereal *, doublereal *, doublereal *, integer *);
    doublereal safmax;
    extern /* Subroutine */ int xerbla_(char *, integer *);
    doublereal bignum;
    extern /* Subroutine */ int dhgeqz_(char *, char *, char *, integer *, 
            integer *, integer *, doublereal *, integer *, doublereal *, 
            integer *, doublereal *, doublereal *, doublereal *, doublereal *, 
             integer *, doublereal *, integer *, doublereal *, integer *, 
            integer *);
    integer ijobvl, iright;
    extern /* Subroutine */ int dtgsen_(integer *, logical *, logical *, 
            logical *, integer *, doublereal *, integer *, doublereal *, 
            integer *, doublereal *, doublereal *, doublereal *, doublereal *, 
             integer *, doublereal *, integer *, integer *, doublereal *, 
            doublereal *, doublereal *, doublereal *, integer *, integer *, 
            integer *, integer *);
    extern integer ilaenv_(integer *, char *, char *, integer *, integer *, 
            integer *, integer *);
    integer ijobvr;
    logical wantsb;
    integer liwmin;
    logical wantse, lastsl;
    doublereal anrmto, bnrmto;
    extern /* Subroutine */ int dorgqr_(integer *, integer *, integer *, 
            doublereal *, integer *, doublereal *, doublereal *, integer *, 
            integer *);
    integer minwrk, maxwrk;
    logical wantsn;
    doublereal smlnum;
    extern /* Subroutine */ int dormqr_(char *, char *, integer *, integer *, 
            integer *, doublereal *, integer *, doublereal *, doublereal *, 
            integer *, doublereal *, integer *, integer *);
    logical wantst, lquery, wantsv;


/*  -- LAPACK driver routine (version 3.2) -- */
/*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/*     November 2006 */

/*     .. Scalar Arguments .. */
/*     .. */
/*     .. Array Arguments .. */
/*     .. */
/*     .. Function Arguments .. */
/*     .. */

/*  Purpose */
/*  ======= */

/*  DGGESX computes for a pair of N-by-N real nonsymmetric matrices */
/*  (A,B), the generalized eigenvalues, the real Schur form (S,T), and, */
/*  optionally, the left and/or right matrices of Schur vectors (VSL and */
/*  VSR).  This gives the generalized Schur factorization */

/*       (A,B) = ( (VSL) S (VSR)**T, (VSL) T (VSR)**T ) */

/*  Optionally, it also orders the eigenvalues so that a selected cluster */
/*  of eigenvalues appears in the leading diagonal blocks of the upper */
/*  quasi-triangular matrix S and the upper triangular matrix T; computes */
/*  a reciprocal condition number for the average of the selected */
/*  eigenvalues (RCONDE); and computes a reciprocal condition number for */
/*  the right and left deflating subspaces corresponding to the selected */
/*  eigenvalues (RCONDV). The leading columns of VSL and VSR then form */
/*  an orthonormal basis for the corresponding left and right eigenspaces */
/*  (deflating subspaces). */

/*  A generalized eigenvalue for a pair of matrices (A,B) is a scalar w */
/*  or a ratio alpha/beta = w, such that  A - w*B is singular.  It is */
/*  usually represented as the pair (alpha,beta), as there is a */
/*  reasonable interpretation for beta=0 or for both being zero. */

/*  A pair of matrices (S,T) is in generalized real Schur form if T is */
/*  upper triangular with non-negative diagonal and S is block upper */
/*  triangular with 1-by-1 and 2-by-2 blocks.  1-by-1 blocks correspond */
/*  to real generalized eigenvalues, while 2-by-2 blocks of S will be */
/*  "standardized" by making the corresponding elements of T have the */
/*  form: */
/*          [  a  0  ] */
/*          [  0  b  ] */

/*  and the pair of corresponding 2-by-2 blocks in S and T will have a */
/*  complex conjugate pair of generalized eigenvalues. */


/*  Arguments */
/*  ========= */

/*  JOBVSL  (input) CHARACTER*1 */
/*          = 'N':  do not compute the left Schur vectors; */
/*          = 'V':  compute the left Schur vectors. */

/*  JOBVSR  (input) CHARACTER*1 */
/*          = 'N':  do not compute the right Schur vectors; */
/*          = 'V':  compute the right Schur vectors. */

/*  SORT    (input) CHARACTER*1 */
/*          Specifies whether or not to order the eigenvalues on the */
/*          diagonal of the generalized Schur form. */
/*          = 'N':  Eigenvalues are not ordered; */
/*          = 'S':  Eigenvalues are ordered (see SELCTG). */

/*  SELCTG  (external procedure) LOGICAL FUNCTION of three DOUBLE PRECISION arguments */
/*          SELCTG must be declared EXTERNAL in the calling subroutine. */
/*          If SORT = 'N', SELCTG is not referenced. */
/*          If SORT = 'S', SELCTG is used to select eigenvalues to sort */
/*          to the top left of the Schur form. */
/*          An eigenvalue (ALPHAR(j)+ALPHAI(j))/BETA(j) is selected if */
/*          SELCTG(ALPHAR(j),ALPHAI(j),BETA(j)) is true; i.e. if either */
/*          one of a complex conjugate pair of eigenvalues is selected, */
/*          then both complex eigenvalues are selected. */
/*          Note that a selected complex eigenvalue may no longer satisfy */
/*          SELCTG(ALPHAR(j),ALPHAI(j),BETA(j)) = .TRUE. after ordering, */
/*          since ordering may change the value of complex eigenvalues */
/*          (especially if the eigenvalue is ill-conditioned), in this */
/*          case INFO is set to N+3. */

/*  SENSE   (input) CHARACTER*1 */
/*          Determines which reciprocal condition numbers are computed. */
/*          = 'N' : None are computed; */
/*          = 'E' : Computed for average of selected eigenvalues only; */
/*          = 'V' : Computed for selected deflating subspaces only; */
/*          = 'B' : Computed for both. */
/*          If SENSE = 'E', 'V', or 'B', SORT must equal 'S'. */

/*  N       (input) INTEGER */
/*          The order of the matrices A, B, VSL, and VSR.  N >= 0. */

/*  A       (input/output) DOUBLE PRECISION array, dimension (LDA, N) */
/*          On entry, the first of the pair of matrices. */
/*          On exit, A has been overwritten by its generalized Schur */
/*          form S. */

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

/*  B       (input/output) DOUBLE PRECISION array, dimension (LDB, N) */
/*          On entry, the second of the pair of matrices. */
/*          On exit, B has been overwritten by its generalized Schur */
/*          form T. */

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

/*  SDIM    (output) INTEGER */
/*          If SORT = 'N', SDIM = 0. */
/*          If SORT = 'S', SDIM = number of eigenvalues (after sorting) */
/*          for which SELCTG is true.  (Complex conjugate pairs for which */
/*          SELCTG is true for either eigenvalue count as 2.) */

/*  ALPHAR  (output) DOUBLE PRECISION array, dimension (N) */
/*  ALPHAI  (output) DOUBLE PRECISION array, dimension (N) */
/*  BETA    (output) DOUBLE PRECISION 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 Schur form of (A,B) were further reduced to */
/*          triangular form using 2-by-2 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. */

/*          Note: the quotients ALPHAR(j)/BETA(j) and ALPHAI(j)/BETA(j) */
/*          may easily over- or underflow, and BETA(j) may even be zero. */
/*          Thus, the user should avoid naively computing the ratio. */
/*          However, ALPHAR and ALPHAI will be always less than and */
/*          usually comparable with norm(A) in magnitude, and BETA always */
/*          less than and usually comparable with norm(B). */

/*  VSL     (output) DOUBLE PRECISION array, dimension (LDVSL,N) */
/*          If JOBVSL = 'V', VSL will contain the left Schur vectors. */
/*          Not referenced if JOBVSL = 'N'. */

/*  LDVSL   (input) INTEGER */
/*          The leading dimension of the matrix VSL. LDVSL >=1, and */
/*          if JOBVSL = 'V', LDVSL >= N. */

/*  VSR     (output) DOUBLE PRECISION array, dimension (LDVSR,N) */
/*          If JOBVSR = 'V', VSR will contain the right Schur vectors. */
/*          Not referenced if JOBVSR = 'N'. */

/*  LDVSR   (input) INTEGER */
/*          The leading dimension of the matrix VSR. LDVSR >= 1, and */
/*          if JOBVSR = 'V', LDVSR >= N. */

/*  RCONDE  (output) DOUBLE PRECISION array, dimension ( 2 ) */
/*          If SENSE = 'E' or 'B', RCONDE(1) and RCONDE(2) contain the */
/*          reciprocal condition numbers for the average of the selected */
/*          eigenvalues. */
/*          Not referenced if SENSE = 'N' or 'V'. */

/*  RCONDV  (output) DOUBLE PRECISION array, dimension ( 2 ) */
/*          If SENSE = 'V' or 'B', RCONDV(1) and RCONDV(2) contain the */
/*          reciprocal condition numbers for the selected deflating */
/*          subspaces. */
/*          Not referenced if SENSE = 'N' or 'E'. */

/*  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. */
/*          If N = 0, LWORK >= 1, else if SENSE = 'E', 'V', or 'B', */
/*          LWORK >= max( 8*N, 6*N+16, 2*SDIM*(N-SDIM) ), else */
/*          LWORK >= max( 8*N, 6*N+16 ). */
/*          Note that 2*SDIM*(N-SDIM) <= N*N/2. */
/*          Note also that an error is only returned if */
/*          LWORK < max( 8*N, 6*N+16), but if SENSE = 'E' or 'V' or 'B' */
/*          this may not be large enough. */

/*          If LWORK = -1, then a workspace query is assumed; the routine */
/*          only calculates the bound on the optimal size of the WORK */
/*          array and the minimum size of the IWORK array, returns these */
/*          values as the first entries of the WORK and IWORK arrays, and */
/*          no error message related to LWORK or LIWORK is issued by */
/*          XERBLA. */

/*  IWORK   (workspace) INTEGER array, dimension (MAX(1,LIWORK)) */
/*          On exit, if INFO = 0, IWORK(1) returns the minimum LIWORK. */

/*  LIWORK  (input) INTEGER */
/*          The dimension of the array IWORK. */
/*          If SENSE = 'N' or N = 0, LIWORK >= 1, otherwise */
/*          LIWORK >= N+6. */

/*          If LIWORK = -1, then a workspace query is assumed; the */
/*          routine only calculates the bound on the optimal size of the */
/*          WORK array and the minimum size of the IWORK array, returns */
/*          these values as the first entries of the WORK and IWORK */
/*          arrays, and no error message related to LWORK or LIWORK is */
/*          issued by XERBLA. */

/*  BWORK   (workspace) LOGICAL array, dimension (N) */
/*          Not referenced if SORT = 'N'. */

/*  INFO    (output) INTEGER */
/*          = 0:  successful exit */
/*          < 0:  if INFO = -i, the i-th argument had an illegal value. */
/*          = 1,...,N: */
/*                The QZ iteration failed.  (A,B) are not in Schur */
/*                form, but ALPHAR(j), ALPHAI(j), and BETA(j) should */
/*                be correct for j=INFO+1,...,N. */
/*          > N:  =N+1: other than QZ iteration failed in DHGEQZ */
/*                =N+2: after reordering, roundoff changed values of */
/*                      some complex eigenvalues so that leading */
/*                      eigenvalues in the Generalized Schur form no */
/*                      longer satisfy SELCTG=.TRUE.  This could also */
/*                      be caused due to scaling. */
/*                =N+3: reordering failed in DTGSEN. */

/*  Further details */
/*  =============== */

/*  An approximate (asymptotic) bound on the average absolute error of */
/*  the selected eigenvalues is */

/*       EPS * norm((A, B)) / RCONDE( 1 ). */

/*  An approximate (asymptotic) bound on the maximum angular error in */
/*  the computed deflating subspaces is */

/*       EPS * norm((A, B)) / RCONDV( 2 ). */

/*  See LAPACK User's Guide, section 4.11 for more information. */

/*  ===================================================================== */

/*     .. Parameters .. */
/*     .. */
/*     .. Local Scalars .. */
/*     .. */
/*     .. Local Arrays .. */
/*     .. */
/*     .. External Subroutines .. */
/*     .. */
/*     .. External Functions .. */
/*     .. */
/*     .. Intrinsic Functions .. */
/*     .. */
/*     .. Executable Statements .. */

/*     Decode the input arguments */

    /* Parameter adjustments */
    a_dim1 = *lda;
    a_offset = 1 + a_dim1;
    a -= a_offset;
    b_dim1 = *ldb;
    b_offset = 1 + b_dim1;
    b -= b_offset;
    --alphar;
    --alphai;
    --beta;
    vsl_dim1 = *ldvsl;
    vsl_offset = 1 + vsl_dim1;
    vsl -= vsl_offset;
    vsr_dim1 = *ldvsr;
    vsr_offset = 1 + vsr_dim1;
    vsr -= vsr_offset;
    --rconde;
    --rcondv;
    --work;
    --iwork;
    --bwork;

    /* Function Body */
    if (lsame_(jobvsl, "N")) {
        ijobvl = 1;
        ilvsl = FALSE_;
    } else if (lsame_(jobvsl, "V")) {
        ijobvl = 2;
        ilvsl = TRUE_;
    } else {
        ijobvl = -1;
        ilvsl = FALSE_;
    }

    if (lsame_(jobvsr, "N")) {
        ijobvr = 1;
        ilvsr = FALSE_;
    } else if (lsame_(jobvsr, "V")) {
        ijobvr = 2;
        ilvsr = TRUE_;
    } else {
        ijobvr = -1;
        ilvsr = FALSE_;
    }

    wantst = lsame_(sort, "S");
    wantsn = lsame_(sense, "N");
    wantse = lsame_(sense, "E");
    wantsv = lsame_(sense, "V");
    wantsb = lsame_(sense, "B");
    lquery = *lwork == -1 || *liwork == -1;
    if (wantsn) {
        ijob = 0;
    } else if (wantse) {
        ijob = 1;
    } else if (wantsv) {
        ijob = 2;
    } else if (wantsb) {
        ijob = 4;
    }

/*     Test the input arguments */

    *info = 0;
    if (ijobvl <= 0) {
        *info = -1;
    } else if (ijobvr <= 0) {
        *info = -2;
    } else if (! wantst && ! lsame_(sort, "N")) {
        *info = -3;
    } else if (! (wantsn || wantse || wantsv || wantsb) || ! wantst && ! 
            wantsn) {
        *info = -5;
    } else if (*n < 0) {
        *info = -6;
    } else if (*lda < max(1,*n)) {
        *info = -8;
    } else if (*ldb < max(1,*n)) {
        *info = -10;
    } else if (*ldvsl < 1 || ilvsl && *ldvsl < *n) {
        *info = -16;
    } else if (*ldvsr < 1 || ilvsr && *ldvsr < *n) {
        *info = -18;
    }

/*     Compute workspace */
/*      (Note: Comments in the code beginning "Workspace:" describe the */
/*       minimal amount of workspace needed at that point in the code, */
/*       as well as the preferred amount for good performance. */
/*       NB refers to the optimal block size for the immediately */
/*       following subroutine, as returned by ILAENV.) */

    if (*info == 0) {
        if (*n > 0) {
/* Computing MAX */
            i__1 = *n << 3, i__2 = *n * 6 + 16;
            minwrk = max(i__1,i__2);
            maxwrk = minwrk - *n + *n * ilaenv_(&c__1, "DGEQRF", " ", n, &
                    c__1, n, &c__0);
/* Computing MAX */
            i__1 = maxwrk, i__2 = minwrk - *n + *n * ilaenv_(&c__1, "DORMQR", 
                    " ", n, &c__1, n, &c_n1);
            maxwrk = max(i__1,i__2);
            if (ilvsl) {
/* Computing MAX */
                i__1 = maxwrk, i__2 = minwrk - *n + *n * ilaenv_(&c__1, "DOR"
                        "GQR", " ", n, &c__1, n, &c_n1);
                maxwrk = max(i__1,i__2);
            }
            lwrk = maxwrk;
            if (ijob >= 1) {
/* Computing MAX */
                i__1 = lwrk, i__2 = *n * *n / 2;
                lwrk = max(i__1,i__2);
            }
        } else {
            minwrk = 1;
            maxwrk = 1;
            lwrk = 1;
        }
        work[1] = (doublereal) lwrk;
        if (wantsn || *n == 0) {
            liwmin = 1;
        } else {
            liwmin = *n + 6;
        }
        iwork[1] = liwmin;

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

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

/*     Quick return if possible */

    if (*n == 0) {
        *sdim = 0;
        return 0;
    }

/*     Get machine constants */

    eps = dlamch_("P");
    safmin = dlamch_("S");
    safmax = 1. / safmin;
    dlabad_(&safmin, &safmax);
    smlnum = sqrt(safmin) / eps;
    bignum = 1. / smlnum;

/*     Scale A if max element outside range [SMLNUM,BIGNUM] */

    anrm = dlange_("M", n, n, &a[a_offset], lda, &work[1]);
    ilascl = FALSE_;
    if (anrm > 0. && anrm < smlnum) {
        anrmto = smlnum;
        ilascl = TRUE_;
    } else if (anrm > bignum) {
        anrmto = bignum;
        ilascl = TRUE_;
    }
    if (ilascl) {
        dlascl_("G", &c__0, &c__0, &anrm, &anrmto, n, n, &a[a_offset], lda, &
                ierr);
    }

/*     Scale B if max element outside range [SMLNUM,BIGNUM] */

    bnrm = dlange_("M", n, n, &b[b_offset], ldb, &work[1]);
    ilbscl = FALSE_;
    if (bnrm > 0. && bnrm < smlnum) {
        bnrmto = smlnum;
        ilbscl = TRUE_;
    } else if (bnrm > bignum) {
        bnrmto = bignum;
        ilbscl = TRUE_;
    }
    if (ilbscl) {
        dlascl_("G", &c__0, &c__0, &bnrm, &bnrmto, n, n, &b[b_offset], ldb, &
                ierr);
    }

/*     Permute the matrix to make it more nearly triangular */
/*     (Workspace: need 6*N + 2*N for permutation parameters) */

    ileft = 1;
    iright = *n + 1;
    iwrk = iright + *n;
    dggbal_("P", n, &a[a_offset], lda, &b[b_offset], ldb, &ilo, &ihi, &work[
            ileft], &work[iright], &work[iwrk], &ierr);

/*     Reduce B to triangular form (QR decomposition of B) */
/*     (Workspace: need N, prefer N*NB) */

    irows = ihi + 1 - ilo;
    icols = *n + 1 - ilo;
    itau = iwrk;
    iwrk = itau + irows;
    i__1 = *lwork + 1 - iwrk;
    dgeqrf_(&irows, &icols, &b[ilo + ilo * b_dim1], ldb, &work[itau], &work[
            iwrk], &i__1, &ierr);

/*     Apply the orthogonal transformation to matrix A */
/*     (Workspace: need N, prefer N*NB) */

    i__1 = *lwork + 1 - iwrk;
    dormqr_("L", "T", &irows, &icols, &irows, &b[ilo + ilo * b_dim1], ldb, &
            work[itau], &a[ilo + ilo * a_dim1], lda, &work[iwrk], &i__1, &
            ierr);

/*     Initialize VSL */
/*     (Workspace: need N, prefer N*NB) */

    if (ilvsl) {
        dlaset_("Full", n, n, &c_b42, &c_b43, &vsl[vsl_offset], ldvsl);
        if (irows > 1) {
            i__1 = irows - 1;
            i__2 = irows - 1;
            dlacpy_("L", &i__1, &i__2, &b[ilo + 1 + ilo * b_dim1], ldb, &vsl[
                    ilo + 1 + ilo * vsl_dim1], ldvsl);
        }
        i__1 = *lwork + 1 - iwrk;
        dorgqr_(&irows, &irows, &irows, &vsl[ilo + ilo * vsl_dim1], ldvsl, &
                work[itau], &work[iwrk], &i__1, &ierr);
    }

/*     Initialize VSR */

    if (ilvsr) {
        dlaset_("Full", n, n, &c_b42, &c_b43, &vsr[vsr_offset], ldvsr);
    }

/*     Reduce to generalized Hessenberg form */
/*     (Workspace: none needed) */

    dgghrd_(jobvsl, jobvsr, n, &ilo, &ihi, &a[a_offset], lda, &b[b_offset], 
            ldb, &vsl[vsl_offset], ldvsl, &vsr[vsr_offset], ldvsr, &ierr);

    *sdim = 0;

/*     Perform QZ algorithm, computing Schur vectors if desired */
/*     (Workspace: need N) */

    iwrk = itau;
    i__1 = *lwork + 1 - iwrk;
    dhgeqz_("S", jobvsl, jobvsr, n, &ilo, &ihi, &a[a_offset], lda, &b[
            b_offset], ldb, &alphar[1], &alphai[1], &beta[1], &vsl[vsl_offset]
, ldvsl, &vsr[vsr_offset], ldvsr, &work[iwrk], &i__1, &ierr);
    if (ierr != 0) {
        if (ierr > 0 && ierr <= *n) {
            *info = ierr;
        } else if (ierr > *n && ierr <= *n << 1) {
            *info = ierr - *n;
        } else {
            *info = *n + 1;
        }
        goto L60;
    }

/*     Sort eigenvalues ALPHA/BETA and compute the reciprocal of */
/*     condition number(s) */
/*     (Workspace: If IJOB >= 1, need MAX( 8*(N+1), 2*SDIM*(N-SDIM) ) */
/*                 otherwise, need 8*(N+1) ) */

    if (wantst) {

/*        Undo scaling on eigenvalues before SELCTGing */

        if (ilascl) {
            dlascl_("G", &c__0, &c__0, &anrmto, &anrm, n, &c__1, &alphar[1], 
                    n, &ierr);
            dlascl_("G", &c__0, &c__0, &anrmto, &anrm, n, &c__1, &alphai[1], 
                    n, &ierr);
        }
        if (ilbscl) {
            dlascl_("G", &c__0, &c__0, &bnrmto, &bnrm, n, &c__1, &beta[1], n, 
                    &ierr);
        }

/*        Select eigenvalues */

        i__1 = *n;
        for (i__ = 1; i__ <= i__1; ++i__) {
            bwork[i__] = (*selctg)(&alphar[i__], &alphai[i__], &beta[i__]);
/* L10: */
        }

/*        Reorder eigenvalues, transform Generalized Schur vectors, and */
/*        compute reciprocal condition numbers */

        i__1 = *lwork - iwrk + 1;
        dtgsen_(&ijob, &ilvsl, &ilvsr, &bwork[1], n, &a[a_offset], lda, &b[
                b_offset], ldb, &alphar[1], &alphai[1], &beta[1], &vsl[
                vsl_offset], ldvsl, &vsr[vsr_offset], ldvsr, sdim, &pl, &pr, 
                dif, &work[iwrk], &i__1, &iwork[1], liwork, &ierr);

        if (ijob >= 1) {
/* Computing MAX */
            i__1 = maxwrk, i__2 = (*sdim << 1) * (*n - *sdim);
            maxwrk = max(i__1,i__2);
        }
        if (ierr == -22) {

/*            not enough real workspace */

            *info = -22;
        } else {
            if (ijob == 1 || ijob == 4) {
                rconde[1] = pl;
                rconde[2] = pr;
            }
            if (ijob == 2 || ijob == 4) {
                rcondv[1] = dif[0];
                rcondv[2] = dif[1];
            }
            if (ierr == 1) {
                *info = *n + 3;
            }
        }

    }

/*     Apply permutation to VSL and VSR */
/*     (Workspace: none needed) */

    if (ilvsl) {
        dggbak_("P", "L", n, &ilo, &ihi, &work[ileft], &work[iright], n, &vsl[
                vsl_offset], ldvsl, &ierr);
    }

    if (ilvsr) {
        dggbak_("P", "R", n, &ilo, &ihi, &work[ileft], &work[iright], n, &vsr[
                vsr_offset], ldvsr, &ierr);
    }

/*     Check if unscaling would cause over/underflow, if so, rescale */
/*     (ALPHAR(I),ALPHAI(I),BETA(I)) so BETA(I) is on the order of */
/*     B(I,I) and ALPHAR(I) and ALPHAI(I) are on the order of A(I,I) */

    if (ilascl) {
        i__1 = *n;
        for (i__ = 1; i__ <= i__1; ++i__) {
            if (alphai[i__] != 0.) {
                if (alphar[i__] / safmax > anrmto / anrm || safmin / alphar[
                        i__] > anrm / anrmto) {
                    work[1] = (d__1 = a[i__ + i__ * a_dim1] / alphar[i__], 
                            abs(d__1));
                    beta[i__] *= work[1];
                    alphar[i__] *= work[1];
                    alphai[i__] *= work[1];
                } else if (alphai[i__] / safmax > anrmto / anrm || safmin / 
                        alphai[i__] > anrm / anrmto) {
                    work[1] = (d__1 = a[i__ + (i__ + 1) * a_dim1] / alphai[
                            i__], abs(d__1));
                    beta[i__] *= work[1];
                    alphar[i__] *= work[1];
                    alphai[i__] *= work[1];
                }
            }
/* L20: */
        }
    }

    if (ilbscl) {
        i__1 = *n;
        for (i__ = 1; i__ <= i__1; ++i__) {
            if (alphai[i__] != 0.) {
                if (beta[i__] / safmax > bnrmto / bnrm || safmin / beta[i__] 
                        > bnrm / bnrmto) {
                    work[1] = (d__1 = b[i__ + i__ * b_dim1] / beta[i__], abs(
                            d__1));
                    beta[i__] *= work[1];
                    alphar[i__] *= work[1];
                    alphai[i__] *= work[1];
                }
            }
/* L30: */
        }
    }

/*     Undo scaling */

    if (ilascl) {
        dlascl_("H", &c__0, &c__0, &anrmto, &anrm, n, n, &a[a_offset], lda, &
                ierr);
        dlascl_("G", &c__0, &c__0, &anrmto, &anrm, n, &c__1, &alphar[1], n, &
                ierr);
        dlascl_("G", &c__0, &c__0, &anrmto, &anrm, n, &c__1, &alphai[1], n, &
                ierr);
    }

    if (ilbscl) {
        dlascl_("U", &c__0, &c__0, &bnrmto, &bnrm, n, n, &b[b_offset], ldb, &
                ierr);
        dlascl_("G", &c__0, &c__0, &bnrmto, &bnrm, n, &c__1, &beta[1], n, &
                ierr);
    }

    if (wantst) {

/*        Check if reordering is correct */

        lastsl = TRUE_;
        lst2sl = TRUE_;
        *sdim = 0;
        ip = 0;
        i__1 = *n;
        for (i__ = 1; i__ <= i__1; ++i__) {
            cursl = (*selctg)(&alphar[i__], &alphai[i__], &beta[i__]);
            if (alphai[i__] == 0.) {
                if (cursl) {
                    ++(*sdim);
                }
                ip = 0;
                if (cursl && ! lastsl) {
                    *info = *n + 2;
                }
            } else {
                if (ip == 1) {

/*                 Last eigenvalue of conjugate pair */

                    cursl = cursl || lastsl;
                    lastsl = cursl;
                    if (cursl) {
                        *sdim += 2;
                    }
                    ip = -1;
                    if (cursl && ! lst2sl) {
                        *info = *n + 2;
                    }
                } else {

/*                 First eigenvalue of conjugate pair */

                    ip = 1;
                }
            }
            lst2sl = lastsl;
            lastsl = cursl;
/* L50: */
        }

    }

L60:

    work[1] = (doublereal) maxwrk;
    iwork[1] = liwmin;

    return 0;

/*     End of DGGESX */

} /* dggesx_ */