dggevx.c

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/* dggevx.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 doublereal c_b59 = 0.;
static doublereal c_b60 = 1.;

/* 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)
{
    /* 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 */
    integer i__, j, m, jc, in, mm, jr;
    doublereal eps;
    logical ilv, pair;
    doublereal anrm, bnrm;
    integer ierr, itau;
    doublereal temp;
    logical ilvl, ilvr;
    integer iwrk, iwrk1;
    extern logical lsame_(char *, char *);
    integer icols;
    logical noscl;
    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 *);
    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 *), dlaset_(char *, integer *, 
            integer *, doublereal *, doublereal *, doublereal *, integer *);
    logical ldumma[1];
    char chtemp[1];
    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 *), dtgevc_(char *, char *, 
            logical *, integer *, doublereal *, integer *, doublereal *, 
            integer *, doublereal *, integer *, doublereal *, integer *, 
            integer *, integer *, doublereal *, integer *);
    integer ijobvl;
    extern /* Subroutine */ int 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 *);
    integer ijobvr;
    logical wantsb;
    extern /* Subroutine */ int dorgqr_(integer *, integer *, integer *, 
            doublereal *, integer *, doublereal *, doublereal *, integer *, 
            integer *);
    doublereal anrmto;
    logical wantse;
    doublereal bnrmto;
    extern /* Subroutine */ int dormqr_(char *, char *, integer *, integer *, 
            integer *, doublereal *, integer *, doublereal *, doublereal *, 
            integer *, doublereal *, integer *, integer *);
    integer minwrk, maxwrk;
    logical wantsn;
    doublereal smlnum;
    logical lquery, wantsv;


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

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

/*  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     (output) INTEGER */
/*  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 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 j-th eigenpair. */
/*          If SENSE = 'N or 'V', RCONDE is not referenced. */

/*  RCONDV  (output) DOUBLE PRECISION array, dimension (N) */
/*          If SENSE = 'V' or 'B', the estimated reciprocal condition */
/*          numbers of the 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 = 'N' or 'E', RCONDV is not referenced. */

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

/*  LWORK   (input) INTEGER */
/*          The dimension of the array WORK. LWORK >= max(1,2*N). */
/*          If BALANC = 'S' or 'B', or JOBVL = 'V', or JOBVR = 'V', */
/*          LWORK >= max(1,6*N). */
/*          If SENSE = 'E' or 'B', LWORK >= max(1,10*N). */
/*          If SENSE = 'V' or 'B', LWORK >= 2*N*N+8*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. */

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

/*     .. 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;
    vl_dim1 = *ldvl;
    vl_offset = 1 + vl_dim1;
    vl -= vl_offset;
    vr_dim1 = *ldvr;
    vr_offset = 1 + vr_dim1;
    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;

    noscl = lsame_(balanc, "N") || lsame_(balanc, "P");
    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.) */

    if (*info == 0) {
        if (*n == 0) {
            minwrk = 1;
            maxwrk = 1;
        } else {
            if (noscl && ! ilv) {
                minwrk = *n << 1;
            } else {
                minwrk = *n * 6;
            }
            if (wantse || wantsb) {
                minwrk = *n * 10;
            }
            if (wantsv || wantsb) {
/* Computing MAX */
                i__1 = minwrk, i__2 = (*n << 1) * (*n + 4) + 16;
                minwrk = max(i__1,i__2);
            }
            maxwrk = minwrk;
/* Computing MAX */
            i__1 = maxwrk, i__2 = *n + *n * ilaenv_(&c__1, "DGEQRF", " ", n, &
                    c__1, n, &c__0);
            maxwrk = max(i__1,i__2);
/* Computing MAX */
            i__1 = maxwrk, i__2 = *n + *n * ilaenv_(&c__1, "DORMQR", " ", n, &
                    c__1, n, &c__0);
            maxwrk = max(i__1,i__2);
            if (ilvl) {
/* Computing MAX */
                i__1 = maxwrk, i__2 = *n + *n * ilaenv_(&c__1, "DORGQR", 
                        " ", n, &c__1, n, &c__0);
                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 if BALANC = 'S' or 'B', 1 otherwise) */

    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[*ilo + *ilo * b_dim1], 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[*ilo + *ilo * b_dim1], ldb, &
            work[itau], &a[*ilo + *ilo * a_dim1], lda, &work[iwrk], &i__1, &
            ierr);

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

    if (ilvl) {
        dlaset_("Full", n, n, &c_b59, &c_b60, &vl[vl_offset], ldvl)
                ;
        if (irows > 1) {
            i__1 = irows - 1;
            i__2 = irows - 1;
            dlacpy_("L", &i__1, &i__2, &b[*ilo + 1 + *ilo * b_dim1], ldb, &vl[
                    *ilo + 1 + *ilo * vl_dim1], ldvl);
        }
        i__1 = *lwork + 1 - iwrk;
        dorgqr_(&irows, &irows, &irows, &vl[*ilo + *ilo * vl_dim1], ldvl, &
                work[itau], &work[iwrk], &i__1, &ierr);
    }

    if (ilvr) {
        dlaset_("Full", n, n, &c_b59, &c_b60, &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[*ilo + *ilo * a_dim1], 
                lda, &b[*ilo + *ilo * b_dim1], 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[i__ + 1 + i__ * a_dim1] != 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[jr + jc * vl_dim1], 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[jr + jc * vl_dim1], abs(
                            d__1)) + (d__2 = vl[jr + (jc + 1) * vl_dim1], 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[jr + jc * vl_dim1] *= temp;
/* L50: */
                }
            } else {
                i__2 = *n;
                for (jr = 1; jr <= i__2; ++jr) {
                    vl[jr + jc * vl_dim1] *= temp;
                    vl[jr + (jc + 1) * vl_dim1] *= 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[jr + jc * vr_dim1], 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[jr + jc * vr_dim1], abs(
                            d__1)) + (d__2 = vr[jr + (jc + 1) * vr_dim1], 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[jr + jc * vr_dim1] *= temp;
/* L100: */
                }
            } else {
                i__2 = *n;
                for (jr = 1; jr <= i__2; ++jr) {
                    vr[jr + jc * vr_dim1] *= temp;
                    vr[jr + (jc + 1) * vr_dim1] *= 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_ */