/src/libsesctherm/CLAPACK/SRC/dggevx.c

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

/* Subroutine */ int dggevx_(char *balanc, char *jobvl, char *jobvr, char *
	sense, integer *n, doublereal *a, integer *lda, doublereal *b, 
	integer *ldb, doublereal *alphar, doublereal *alphai, doublereal *
	beta, doublereal *vl, integer *ldvl, doublereal *vr, integer *ldvr, 
	integer *ilo, integer *ihi, doublereal *lscale, doublereal *rscale, 
	doublereal *abnrm, doublereal *bbnrm, doublereal *rconde, doublereal *
	rcondv, doublereal *work, integer *lwork, integer *iwork, logical *
	bwork, integer *info)
{
/*  -- LAPACK driver 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   
    =======   

    DGGEVX computes for a pair of N-by-N real nonsymmetric matrices (A,B)   
    the generalized eigenvalues, and optionally, the left and/or right   
    generalized eigenvectors.   

    Optionally also, it computes a balancing transformation to improve   
    the conditioning of the eigenvalues and eigenvectors (ILO, IHI,   
    LSCALE, RSCALE, ABNRM, and BBNRM), reciprocal condition numbers for   
    the eigenvalues (RCONDE), and reciprocal condition numbers for the   
    right eigenvectors (RCONDV).   

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

    The right eigenvector v(j) corresponding to the eigenvalue lambda(j)   
    of (A,B) satisfies   

                     A * v(j) = lambda(j) * B * v(j) .   

    The left eigenvector u(j) corresponding to the eigenvalue lambda(j)   
    of (A,B) satisfies   

                     u(j)**H * A  = lambda(j) * u(j)**H * B.   

    where u(j)**H is the conjugate-transpose of u(j).   


    Arguments   
    =========   

    BALANC  (input) CHARACTER*1   
            Specifies the balance option to be performed.   
            = 'N':  do not diagonally scale or permute;   
            = 'P':  permute only;   
            = 'S':  scale only;   
            = 'B':  both permute and scale.   
            Computed reciprocal condition numbers will be for the   
            matrices after permuting and/or balancing. Permuting does   
            not change condition numbers (in exact arithmetic), but   
            balancing does.   

    JOBVL   (input) CHARACTER*1   
            = 'N':  do not compute the left generalized eigenvectors;   
            = 'V':  compute the left generalized eigenvectors.   

    JOBVR   (input) CHARACTER*1   
            = 'N':  do not compute the right generalized eigenvectors;   
            = 'V':  compute the right generalized eigenvectors.   

    SENSE   (input) CHARACTER*1   
            Determines which reciprocal condition numbers are computed.   
            = 'N': none are computed;   
            = 'E': computed for eigenvalues only;   
            = 'V': computed for eigenvectors only;   
            = 'B': computed for eigenvalues and eigenvectors.   

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

    A       (input/output) DOUBLE PRECISION array, dimension (LDA, N)   
            On entry, the matrix A in the pair (A,B).   
            On exit, A has been overwritten. If JOBVL='V' or JOBVR='V'   
            or both, then A contains the first part of the real Schur   
            form of the "balanced" versions of the input A and B.   

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

    B       (input/output) DOUBLE PRECISION array, dimension (LDB, N)   
            On entry, the matrix B in the pair (A,B).   
            On exit, B has been overwritten. If JOBVL='V' or JOBVR='V'   
            or both, then B contains the second part of the real Schur   
            form of the "balanced" versions of the input A and B.   

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

    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.  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   
            ALPHA/BETA. 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).   

    VL      (output) DOUBLE PRECISION array, dimension (LDVL,N)   
            If JOBVL = 'V', the left eigenvectors u(j) are stored one   
            after another in the columns of VL, in the same order as   
            their eigenvalues. If the j-th eigenvalue is real, then   
            u(j) = VL(:,j), the j-th column of VL. If the j-th and   
            (j+1)-th eigenvalues form a complex conjugate pair, then   
            u(j) = VL(:,j)+i*VL(:,j+1) and u(j+1) = VL(:,j)-i*VL(:,j+1).   
            Each eigenvector will be scaled so the largest component have   
            abs(real part) + abs(imag. part) = 1.   
            Not referenced if JOBVL = 'N'.   

    LDVL    (input) INTEGER   
            The leading dimension of the matrix VL. LDVL >= 1, and   
            if JOBVL = 'V', LDVL >= N.   

    VR      (output) DOUBLE PRECISION array, dimension (LDVR,N)   
            If JOBVR = 'V', the right eigenvectors v(j) are stored one   
            after another in the columns of VR, in the same order as   
            their eigenvalues. If the j-th eigenvalue is real, then   
            v(j) = VR(:,j), the j-th column of VR. If the j-th and   
            (j+1)-th eigenvalues form a complex conjugate pair, then   
            v(j) = VR(:,j)+i*VR(:,j+1) and v(j+1) = VR(:,j)-i*VR(:,j+1).   
            Each eigenvector will be scaled so the largest component have   
            abs(real part) + abs(imag. part) = 1.   
            Not referenced if JOBVR = 'N'.   

    LDVR    (input) INTEGER   
            The leading dimension of the matrix VR. LDVR >= 1, and   
            if JOBVR = 'V', LDVR >= N.   

    ILO,IHI (output) INTEGER   
            ILO and IHI are integer values such that on exit   
            A(i,j) = 0 and B(i,j) = 0 if i > j and   
            j = 1,...,ILO-1 or i = IHI+1,...,N.   
            If BALANC = 'N' or 'S', ILO = 1 and IHI = N.   

    LSCALE  (output) DOUBLE PRECISION array, dimension (N)   
            Details of the permutations and scaling factors applied   
            to the left side of A and B.  If PL(j) is the index of the   
            row interchanged with row j, and DL(j) is the scaling   
            factor applied to row j, then   
              LSCALE(j) = PL(j)  for j = 1,...,ILO-1   
                        = DL(j)  for j = ILO,...,IHI   
                        = PL(j)  for j = IHI+1,...,N.   
            The order in which the interchanges are made is N to IHI+1,   
            then 1 to ILO-1.   

    RSCALE  (output) DOUBLE PRECISION array, dimension (N)   
            Details of the permutations and scaling factors applied   
            to the right side of A and B.  If PR(j) is the index of the   
            column interchanged with column j, and DR(j) is the scaling   
            factor applied to column j, then   
              RSCALE(j) = PR(j)  for j = 1,...,ILO-1   
                        = DR(j)  for j = ILO,...,IHI   
                        = PR(j)  for j = IHI+1,...,N   
            The order in which the interchanges are made is N to IHI+1,   
            then 1 to ILO-1.   

    ABNRM   (output) DOUBLE PRECISION   
            The one-norm of the balanced matrix A.   

    BBNRM   (output) DOUBLE PRECISION   
            The one-norm of the balanced matrix B.   

    RCONDE  (output) DOUBLE PRECISION array, dimension (N)   
            If SENSE = 'E' or 'B', the reciprocal condition numbers of   
            the selected eigenvalues, stored in consecutive elements of   
            the array. For a complex conjugate pair of eigenvalues two   
            consecutive elements of RCONDE are set to the same value.   
            Thus RCONDE(j), RCONDV(j), and the j-th columns of VL and VR   
            all correspond to the same eigenpair (but not in general the   
            j-th eigenpair, unless all eigenpairs are selected).   
            If SENSE = 'V', RCONDE is not referenced.   

    RCONDV  (output) DOUBLE PRECISION array, dimension (N)   
            If SENSE = 'V' or 'B', the estimated reciprocal condition   
            numbers of the selected eigenvectors, stored in consecutive   
            elements of the array. For a complex eigenvector two   
            consecutive elements of RCONDV are set to the same value. If   
            the eigenvalues cannot be reordered to compute RCONDV(j),   
            RCONDV(j) is set to 0; this can only occur when the true   
            value would be very small anyway.   
            If SENSE = 'E', RCONDV is not referenced.   

    WORK    (workspace/output) DOUBLE PRECISION array, dimension (LWORK)   
            On exit, if INFO = 0, WORK(1) returns the optimal LWORK.   

    LWORK   (input) INTEGER   
            The dimension of the array WORK. LWORK >= max(1,6*N).   
            If SENSE = 'E', LWORK >= 12*N.   
            If SENSE = 'V' or 'B', LWORK >= 2*N*N+12*N+16.   

            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) INTEGER array, dimension (N+6)   
            If SENSE = 'E', IWORK is not referenced.   

    BWORK   (workspace) LOGICAL array, dimension (N)   
            If SENSE = 'N', BWORK is not referenced.   

    INFO    (output) INTEGER   
            = 0:  successful exit   
            < 0:  if INFO = -i, the i-th argument had an illegal value.   
            = 1,...,N:   
                  The QZ iteration failed.  No eigenvectors have been   
                  calculated, 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: error return from DTGEVC.   

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

    Balancing a matrix pair (A,B) includes, first, permuting rows and   
    columns to isolate eigenvalues, second, applying diagonal similarity   
    transformation to the rows and columns to make the rows and columns   
    as close in norm as possible. The computed reciprocal condition   
    numbers correspond to the balanced matrix. Permuting rows and columns   
    will not change the condition numbers (in exact arithmetic) but   
    diagonal scaling will.  For further explanation of balancing, see   
    section 4.11.1.2 of LAPACK Users' Guide.   

    An approximate error bound on the chordal distance between the i-th   
    computed generalized eigenvalue w and the corresponding exact   
    eigenvalue lambda is   

         chord(w, lambda) <= EPS * norm(ABNRM, BBNRM) / RCONDE(I)   

    An approximate error bound for the angle between the i-th computed   
    eigenvector VL(i) or VR(i) is given by   

         EPS * norm(ABNRM, BBNRM) / DIF(i).   

    For further explanation of the reciprocal condition numbers RCONDE   
    and RCONDV, see section 4.11 of LAPACK User's Guide.   

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


       Decode the input arguments   

       Parameter adjustments */
    /* Table of constant values */
    static integer c__1 = 1;
    static integer c__0 = 0;
    static doublereal c_b47 = 0.;
    static doublereal c_b48 = 1.;
    
    /* System generated locals */
    integer a_dim1, a_offset, b_dim1, b_offset, vl_dim1, vl_offset, vr_dim1, 
	    vr_offset, i__1, i__2;
    doublereal d__1, d__2, d__3, d__4;
    /* Builtin functions */
    double sqrt(doublereal);
    /* Local variables */
    static logical pair;
    static doublereal anrm, bnrm;
    static integer ierr, itau;
    static doublereal temp;
    static logical ilvl, ilvr;
    static integer iwrk, iwrk1, i__, j, m;
    extern logical lsame_(char *, char *);
    static integer icols, irows;
    extern /* Subroutine */ int dlabad_(doublereal *, doublereal *);
    static integer jc;
    extern /* Subroutine */ int 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 *);
    static integer in;
    extern doublereal dlamch_(char *);
    static integer mm;
    extern doublereal dlange_(char *, integer *, integer *, doublereal *, 
	    integer *, doublereal *);
    static integer jr;
    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 *);
    static logical ilascl, ilbscl;
    extern /* Subroutine */ int dgeqrf_(integer *, integer *, doublereal *, 
	    integer *, doublereal *, doublereal *, integer *, integer *), 
	    dlacpy_(char *, integer *, integer *, doublereal *, integer *, 
	    doublereal *, integer *);
    static logical ldumma[1];
    static char chtemp[1];
    static 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 *), dlaset_(char *, integer *, 
	    integer *, doublereal *, doublereal *, doublereal *, integer *);
    static integer ijobvl;
    extern /* Subroutine */ int dtgevc_(char *, char *, logical *, integer *, 
	    doublereal *, integer *, doublereal *, integer *, doublereal *, 
	    integer *, doublereal *, integer *, integer *, integer *, 
	    doublereal *, integer *), dtgsna_(char *, char *, 
	    logical *, integer *, doublereal *, integer *, doublereal *, 
	    integer *, doublereal *, integer *, doublereal *, integer *, 
	    doublereal *, doublereal *, integer *, integer *, doublereal *, 
	    integer *, integer *, integer *), xerbla_(char *, 
	    integer *);
    extern integer ilaenv_(integer *, char *, char *, integer *, integer *, 
	    integer *, integer *, ftnlen, ftnlen);
    static integer ijobvr;
    static logical wantsb;
    extern /* Subroutine */ int dorgqr_(integer *, integer *, integer *, 
	    doublereal *, integer *, doublereal *, doublereal *, integer *, 
	    integer *);
    static doublereal anrmto;
    static logical wantse;
    static doublereal bnrmto;
    extern /* Subroutine */ int dormqr_(char *, char *, integer *, integer *, 
	    integer *, doublereal *, integer *, doublereal *, doublereal *, 
	    integer *, doublereal *, integer *, integer *);
    static integer minwrk, maxwrk;
    static logical wantsn;
    static doublereal smlnum;
    static logical lquery, wantsv;
    static doublereal eps;
    static logical ilv;
#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 vl_ref(a_1,a_2) vl[(a_2)*vl_dim1 + a_1]
#define vr_ref(a_1,a_2) vr[(a_2)*vr_dim1 + a_1]


    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;
    vl_dim1 = *ldvl;
    vl_offset = 1 + vl_dim1 * 1;
    vl -= vl_offset;
    vr_dim1 = *ldvr;
    vr_offset = 1 + vr_dim1 * 1;
    vr -= vr_offset;
    --lscale;
    --rscale;
    --rconde;
    --rcondv;
    --work;
    --iwork;
    --bwork;

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

    if (lsame_(jobvr, "N")) {
	ijobvr = 1;
	ilvr = FALSE_;
    } else if (lsame_(jobvr, "V")) {
	ijobvr = 2;
	ilvr = TRUE_;
    } else {
	ijobvr = -1;
	ilvr = FALSE_;
    }
    ilv = ilvl || ilvr;

    wantsn = lsame_(sense, "N");
    wantse = lsame_(sense, "E");
    wantsv = lsame_(sense, "V");
    wantsb = lsame_(sense, "B");

/*     Test the input arguments */

    *info = 0;
    lquery = *lwork == -1;
    if (! (lsame_(balanc, "N") || lsame_(balanc, "S") || lsame_(balanc, "P") 
	    || lsame_(balanc, "B"))) {
	*info = -1;
    } else if (ijobvl <= 0) {
	*info = -2;
    } else if (ijobvr <= 0) {
	*info = -3;
    } else if (! (wantsn || wantse || wantsb || wantsv)) {
	*info = -4;
    } else if (*n < 0) {
	*info = -5;
    } else if (*lda < max(1,*n)) {
	*info = -7;
    } else if (*ldb < max(1,*n)) {
	*info = -9;
    } else if (*ldvl < 1 || ilvl && *ldvl < *n) {
	*info = -14;
    } else if (*ldvr < 1 || ilvr && *ldvr < *n) {
	*info = -16;
    }

/*     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. The workspace is   
         computed assuming ILO = 1 and IHI = N, the worst case.) */

    minwrk = 1;
    if (*info == 0 && (*lwork >= 1 || lquery)) {
	maxwrk = *n * 5 + *n * ilaenv_(&c__1, "DGEQRF", " ", n, &c__1, n, &
		c__0, (ftnlen)6, (ftnlen)1);
/* Computing MAX */
	i__1 = 1, i__2 = *n * 6;
	minwrk = max(i__1,i__2);
	if (wantse) {
/* Computing MAX */
	    i__1 = 1, i__2 = *n * 12;
	    minwrk = max(i__1,i__2);
	} else if (wantsv || wantsb) {
	    minwrk = (*n << 1) * *n + *n * 12 + 16;
/* Computing MAX */
	    i__1 = maxwrk, i__2 = (*n << 1) * *n + *n * 12 + 16;
	    maxwrk = max(i__1,i__2);
	}
	work[1] = (doublereal) maxwrk;
    }

    if (*lwork < minwrk && ! lquery) {
	*info = -26;
    }

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

/*     Quick return if possible */

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


/*     Get machine constants */

    eps = dlamch_("P");
    smlnum = dlamch_("S");
    bignum = 1. / smlnum;
    dlabad_(&smlnum, &bignum);
    smlnum = sqrt(smlnum) / 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 and/or balance the matrix pair (A,B)   
       (Workspace: need 6*N) */

    dggbal_(balanc, n, &a[a_offset], lda, &b[b_offset], ldb, ilo, ihi, &
	    lscale[1], &rscale[1], &work[1], &ierr);

/*     Compute ABNRM and BBNRM */

    *abnrm = dlange_("1", n, n, &a[a_offset], lda, &work[1]);
    if (ilascl) {
	work[1] = *abnrm;
	dlascl_("G", &c__0, &c__0, &anrmto, &anrm, &c__1, &c__1, &work[1], &
		c__1, &ierr);
	*abnrm = work[1];
    }

    *bbnrm = dlange_("1", n, n, &b[b_offset], ldb, &work[1]);
    if (ilbscl) {
	work[1] = *bbnrm;
	dlascl_("G", &c__0, &c__0, &bnrmto, &bnrm, &c__1, &c__1, &work[1], &
		c__1, &ierr);
	*bbnrm = work[1];
    }

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

    irows = *ihi + 1 - *ilo;
    if (ilv || ! wantsn) {
	icols = *n + 1 - *ilo;
    } else {
	icols = irows;
    }
    itau = 1;
    iwrk = itau + irows;
    i__1 = *lwork + 1 - iwrk;
    dgeqrf_(&irows, &icols, &b_ref(*ilo, *ilo), ldb, &work[itau], &work[iwrk],
	     &i__1, &ierr);

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

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

/*     Initialize VL and/or VR   
       (Workspace: need N, prefer N*NB) */

    if (ilvl) {
	dlaset_("Full", n, n, &c_b47, &c_b48, &vl[vl_offset], ldvl)
		;
	i__1 = irows - 1;
	i__2 = irows - 1;
	dlacpy_("L", &i__1, &i__2, &b_ref(*ilo + 1, *ilo), ldb, &vl_ref(*ilo 
		+ 1, *ilo), ldvl);
	i__1 = *lwork + 1 - iwrk;
	dorgqr_(&irows, &irows, &irows, &vl_ref(*ilo, *ilo), ldvl, &work[itau]
		, &work[iwrk], &i__1, &ierr);
    }

    if (ilvr) {
	dlaset_("Full", n, n, &c_b47, &c_b48, &vr[vr_offset], ldvr)
		;
    }

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

    if (ilv || ! wantsn) {

/*        Eigenvectors requested -- work on whole matrix. */

	dgghrd_(jobvl, jobvr, n, ilo, ihi, &a[a_offset], lda, &b[b_offset], 
		ldb, &vl[vl_offset], ldvl, &vr[vr_offset], ldvr, &ierr);
    } else {
	dgghrd_("N", "N", &irows, &c__1, &irows, &a_ref(*ilo, *ilo), lda, &
		b_ref(*ilo, *ilo), ldb, &vl[vl_offset], ldvl, &vr[vr_offset], 
		ldvr, &ierr);
    }

/*     Perform QZ algorithm (Compute eigenvalues, and optionally, the   
       Schur forms and Schur vectors)   
       (Workspace: need N) */

    if (ilv || ! wantsn) {
	*(unsigned char *)chtemp = 'S';
    } else {
	*(unsigned char *)chtemp = 'E';
    }

    dhgeqz_(chtemp, jobvl, jobvr, n, ilo, ihi, &a[a_offset], lda, &b[b_offset]
	    , ldb, &alphar[1], &alphai[1], &beta[1], &vl[vl_offset], ldvl, &
	    vr[vr_offset], ldvr, &work[1], lwork, &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 L130;
    }

/*     Compute Eigenvectors and estimate condition numbers if desired   
       (Workspace: DTGEVC: need 6*N   
                   DTGSNA: need 2*N*(N+2)+16 if SENSE = 'V' or 'B',   
                           need N otherwise ) */

    if (ilv || ! wantsn) {
	if (ilv) {
	    if (ilvl) {
		if (ilvr) {
		    *(unsigned char *)chtemp = 'B';
		} else {
		    *(unsigned char *)chtemp = 'L';
		}
	    } else {
		*(unsigned char *)chtemp = 'R';
	    }

	    dtgevc_(chtemp, "B", ldumma, n, &a[a_offset], lda, &b[b_offset], 
		    ldb, &vl[vl_offset], ldvl, &vr[vr_offset], ldvr, n, &in, &
		    work[1], &ierr);
	    if (ierr != 0) {
		*info = *n + 2;
		goto L130;
	    }
	}

	if (! wantsn) {

/*           compute eigenvectors (DTGEVC) and estimate condition   
             numbers (DTGSNA). Note that the definition of the condition   
             number is not invariant under transformation (u,v) to   
             (Q*u, Z*v), where (u,v) are eigenvectors of the generalized   
             Schur form (S,T), Q and Z are orthogonal matrices. In order   
             to avoid using extra 2*N*N workspace, we have to recalculate   
             eigenvectors and estimate one condition numbers at a time. */

	    pair = FALSE_;
	    i__1 = *n;
	    for (i__ = 1; i__ <= i__1; ++i__) {

		if (pair) {
		    pair = FALSE_;
		    goto L20;
		}
		mm = 1;
		if (i__ < *n) {
		    if (a_ref(i__ + 1, i__) != 0.) {
			pair = TRUE_;
			mm = 2;
		    }
		}

		i__2 = *n;
		for (j = 1; j <= i__2; ++j) {
		    bwork[j] = FALSE_;
/* L10: */
		}
		if (mm == 1) {
		    bwork[i__] = TRUE_;
		} else if (mm == 2) {
		    bwork[i__] = TRUE_;
		    bwork[i__ + 1] = TRUE_;
		}

		iwrk = mm * *n + 1;
		iwrk1 = iwrk + mm * *n;

/*              Compute a pair of left and right eigenvectors.   
                (compute workspace: need up to 4*N + 6*N) */

		if (wantse || wantsb) {
		    dtgevc_("B", "S", &bwork[1], n, &a[a_offset], lda, &b[
			    b_offset], ldb, &work[1], n, &work[iwrk], n, &mm, 
			    &m, &work[iwrk1], &ierr);
		    if (ierr != 0) {
			*info = *n + 2;
			goto L130;
		    }
		}

		i__2 = *lwork - iwrk1 + 1;
		dtgsna_(sense, "S", &bwork[1], n, &a[a_offset], lda, &b[
			b_offset], ldb, &work[1], n, &work[iwrk], n, &rconde[
			i__], &rcondv[i__], &mm, &m, &work[iwrk1], &i__2, &
			iwork[1], &ierr);

L20:
		;
	    }
	}
    }

/*     Undo balancing on VL and VR and normalization   
       (Workspace: none needed) */

    if (ilvl) {
	dggbak_(balanc, "L", n, ilo, ihi, &lscale[1], &rscale[1], n, &vl[
		vl_offset], ldvl, &ierr);

	i__1 = *n;
	for (jc = 1; jc <= i__1; ++jc) {
	    if (alphai[jc] < 0.) {
		goto L70;
	    }
	    temp = 0.;
	    if (alphai[jc] == 0.) {
		i__2 = *n;
		for (jr = 1; jr <= i__2; ++jr) {
/* Computing MAX */
		    d__2 = temp, d__3 = (d__1 = vl_ref(jr, jc), abs(d__1));
		    temp = max(d__2,d__3);
/* L30: */
		}
	    } else {
		i__2 = *n;
		for (jr = 1; jr <= i__2; ++jr) {
/* Computing MAX */
		    d__3 = temp, d__4 = (d__1 = vl_ref(jr, jc), abs(d__1)) + (
			    d__2 = vl_ref(jr, jc + 1), abs(d__2));
		    temp = max(d__3,d__4);
/* L40: */
		}
	    }
	    if (temp < smlnum) {
		goto L70;
	    }
	    temp = 1. / temp;
	    if (alphai[jc] == 0.) {
		i__2 = *n;
		for (jr = 1; jr <= i__2; ++jr) {
		    vl_ref(jr, jc) = vl_ref(jr, jc) * temp;
/* L50: */
		}
	    } else {
		i__2 = *n;
		for (jr = 1; jr <= i__2; ++jr) {
		    vl_ref(jr, jc) = vl_ref(jr, jc) * temp;
		    vl_ref(jr, jc + 1) = vl_ref(jr, jc + 1) * temp;
/* L60: */
		}
	    }
L70:
	    ;
	}
    }
    if (ilvr) {
	dggbak_(balanc, "R", n, ilo, ihi, &lscale[1], &rscale[1], n, &vr[
		vr_offset], ldvr, &ierr);
	i__1 = *n;
	for (jc = 1; jc <= i__1; ++jc) {
	    if (alphai[jc] < 0.) {
		goto L120;
	    }
	    temp = 0.;
	    if (alphai[jc] == 0.) {
		i__2 = *n;
		for (jr = 1; jr <= i__2; ++jr) {
/* Computing MAX */
		    d__2 = temp, d__3 = (d__1 = vr_ref(jr, jc), abs(d__1));
		    temp = max(d__2,d__3);
/* L80: */
		}
	    } else {
		i__2 = *n;
		for (jr = 1; jr <= i__2; ++jr) {
/* Computing MAX */
		    d__3 = temp, d__4 = (d__1 = vr_ref(jr, jc), abs(d__1)) + (
			    d__2 = vr_ref(jr, jc + 1), abs(d__2));
		    temp = max(d__3,d__4);
/* L90: */
		}
	    }
	    if (temp < smlnum) {
		goto L120;
	    }
	    temp = 1. / temp;
	    if (alphai[jc] == 0.) {
		i__2 = *n;
		for (jr = 1; jr <= i__2; ++jr) {
		    vr_ref(jr, jc) = vr_ref(jr, jc) * temp;
/* L100: */
		}
	    } else {
		i__2 = *n;
		for (jr = 1; jr <= i__2; ++jr) {
		    vr_ref(jr, jc) = vr_ref(jr, jc) * temp;
		    vr_ref(jr, jc + 1) = vr_ref(jr, jc + 1) * temp;
/* L110: */
		}
	    }
L120:
	    ;
	}
    }

/*     Undo scaling if necessary */

    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);
    }

L130:
    work[1] = (doublereal) maxwrk;

    return 0;

/*     End of DGGEVX */

} /* dggevx_ */

#undef vr_ref
#undef vl_ref
#undef b_ref
#undef a_ref