sgegv.c

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/* sgegv.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_n1 = -1;
static real c_b27 = 1.f;
static real c_b38 = 0.f;

/* Subroutine */ int sgegv_(char *jobvl, char *jobvr, integer *n, real *a, 
        integer *lda, real *b, integer *ldb, real *alphar, real *alphai, real 
        *beta, real *vl, integer *ldvl, real *vr, integer *ldvr, real *work, 
        integer *lwork, 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;
    real r__1, r__2, r__3, r__4;

    /* Local variables */
    integer jc, nb, in, jr, nb1, nb2, nb3, ihi, ilo;
    real eps;
    logical ilv;
    real absb, anrm, bnrm;
    integer itau;
    real temp;
    logical ilvl, ilvr;
    integer lopt;
    real anrm1, anrm2, bnrm1, bnrm2, absai, scale, absar, sbeta;
    extern logical lsame_(char *, char *);
    integer ileft, iinfo, icols, iwork, irows;
    real salfai;
    extern /* Subroutine */ int sggbak_(char *, char *, integer *, integer *, 
            integer *, real *, real *, integer *, real *, integer *, integer *
), sggbal_(char *, integer *, real *, integer *, 
            real *, integer *, integer *, integer *, real *, real *, real *, 
            integer *);
    real salfar;
    extern doublereal slamch_(char *), slange_(char *, integer *, 
            integer *, real *, integer *, real *);
    real safmin;
    extern /* Subroutine */ int sgghrd_(char *, char *, integer *, integer *, 
            integer *, real *, integer *, real *, integer *, real *, integer *
, real *, integer *, integer *);
    real safmax;
    char chtemp[1];
    logical ldumma[1];
    extern /* Subroutine */ int slascl_(char *, integer *, integer *, real *, 
            real *, integer *, integer *, real *, integer *, integer *), xerbla_(char *, integer *);
    extern integer ilaenv_(integer *, char *, char *, integer *, integer *, 
            integer *, integer *);
    integer ijobvl, iright;
    logical ilimit;
    extern /* Subroutine */ int sgeqrf_(integer *, integer *, real *, integer 
            *, real *, real *, integer *, integer *);
    integer ijobvr;
    extern /* Subroutine */ int slacpy_(char *, integer *, integer *, real *, 
            integer *, real *, integer *), slaset_(char *, integer *, 
            integer *, real *, real *, real *, integer *), stgevc_(
            char *, char *, logical *, integer *, real *, integer *, real *, 
            integer *, real *, integer *, real *, integer *, integer *, 
            integer *, real *, integer *);
    real onepls;
    integer lwkmin;
    extern /* Subroutine */ int shgeqz_(char *, char *, char *, integer *, 
            integer *, integer *, real *, integer *, real *, integer *, real *
, real *, real *, real *, integer *, real *, integer *, real *, 
            integer *, integer *), sorgqr_(integer *, 
            integer *, integer *, real *, integer *, real *, real *, integer *
, integer *);
    integer lwkopt;
    logical lquery;
    extern /* Subroutine */ int sormqr_(char *, char *, integer *, integer *, 
            integer *, real *, integer *, real *, real *, integer *, real *, 
            integer *, integer *);


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

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

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

/*  This routine is deprecated and has been replaced by routine SGGEV. */

/*  SGEGV computes the eigenvalues and, optionally, the left and/or right */
/*  eigenvectors of a real matrix pair (A,B). */
/*  Given two square matrices A and B, */
/*  the generalized nonsymmetric eigenvalue problem (GNEP) is to find the */
/*  eigenvalues lambda and corresponding (non-zero) eigenvectors x such */
/*  that */

/*     A*x = lambda*B*x. */

/*  An alternate form is to find the eigenvalues mu and corresponding */
/*  eigenvectors y such that */

/*     mu*A*y = B*y. */

/*  These two forms are equivalent with mu = 1/lambda and x = y if */
/*  neither lambda nor mu is zero.  In order to deal with the case that */
/*  lambda or mu is zero or small, two values alpha and beta are returned */
/*  for each eigenvalue, such that lambda = alpha/beta and */
/*  mu = beta/alpha. */

/*  The vectors x and y in the above equations are right eigenvectors of */
/*  the matrix pair (A,B).  Vectors u and v satisfying */

/*     u**H*A = lambda*u**H*B  or  mu*v**H*A = v**H*B */

/*  are left eigenvectors of (A,B). */

/*  Note: this routine performs "full balancing" on A and B -- see */
/*  "Further Details", below. */

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

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

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

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

/*  A       (input/output) REAL array, dimension (LDA, N) */
/*          On entry, the matrix A. */
/*          If JOBVL = 'V' or JOBVR = 'V', then on exit A */
/*          contains the real Schur form of A from the generalized Schur */
/*          factorization of the pair (A,B) after balancing. */
/*          If no eigenvectors were computed, then only the diagonal */
/*          blocks from the Schur form will be correct.  See SGGHRD and */
/*          SHGEQZ for details. */

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

/*  B       (input/output) REAL array, dimension (LDB, N) */
/*          On entry, the matrix B. */
/*          If JOBVL = 'V' or JOBVR = 'V', then on exit B contains the */
/*          upper triangular matrix obtained from B in the generalized */
/*          Schur factorization of the pair (A,B) after balancing. */
/*          If no eigenvectors were computed, then only those elements of */
/*          B corresponding to the diagonal blocks from the Schur form of */
/*          A will be correct.  See SGGHRD and SHGEQZ for details. */

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

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

/*  ALPHAI  (output) REAL array, dimension (N) */
/*          The imaginary parts of each scalar alpha defining an */
/*          eigenvalue of GNEP.  If ALPHAI(j) is zero, then the j-th */
/*          eigenvalue is real; if positive, then the j-th and */
/*          (j+1)-st eigenvalues are a complex conjugate pair, with */
/*          ALPHAI(j+1) = -ALPHAI(j). */

/*  BETA    (output) REAL array, dimension (N) */
/*          The scalars beta that define the eigenvalues of GNEP. */

/*          Together, the quantities alpha = (ALPHAR(j),ALPHAI(j)) and */
/*          beta = BETA(j) represent the j-th eigenvalue of the matrix */
/*          pair (A,B), in one of the forms lambda = alpha/beta or */
/*          mu = beta/alpha.  Since either lambda or mu may overflow, */
/*          they should not, in general, be computed. */

/*  VL      (output) REAL array, dimension (LDVL,N) */
/*          If JOBVL = 'V', the left eigenvectors u(j) are stored */
/*          in the columns of VL, in the same order as their eigenvalues. */
/*          If the j-th eigenvalue is real, then u(j) = VL(:,j). */
/*          If the j-th and (j+1)-st 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 is scaled so that its largest component has */
/*          abs(real part) + abs(imag. part) = 1, except for eigenvectors */
/*          corresponding to an eigenvalue with alpha = beta = 0, which */
/*          are set to zero. */
/*          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) REAL array, dimension (LDVR,N) */
/*          If JOBVR = 'V', the right eigenvectors x(j) are stored */
/*          in the columns of VR, in the same order as their eigenvalues. */
/*          If the j-th eigenvalue is real, then x(j) = VR(:,j). */
/*          If the j-th and (j+1)-st eigenvalues form a complex conjugate */
/*          pair, then */
/*            x(j) = VR(:,j) + i*VR(:,j+1) */
/*          and */
/*            x(j+1) = VR(:,j) - i*VR(:,j+1). */

/*          Each eigenvector is scaled so that its largest component has */
/*          abs(real part) + abs(imag. part) = 1, except for eigenvalues */
/*          corresponding to an eigenvalue with alpha = beta = 0, which */
/*          are set to zero. */
/*          Not referenced if JOBVR = 'N'. */

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

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

/*  LWORK   (input) INTEGER */
/*          The dimension of the array WORK.  LWORK >= max(1,8*N). */
/*          For good performance, LWORK must generally be larger. */
/*          To compute the optimal value of LWORK, call ILAENV to get */
/*          blocksizes (for SGEQRF, SORMQR, and SORGQR.)  Then compute: */
/*          NB  -- MAX of the blocksizes for SGEQRF, SORMQR, and SORGQR; */
/*          The optimal LWORK is: */
/*              2*N + MAX( 6*N, N*(NB+1) ). */

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

/*  INFO    (output) INTEGER */
/*          = 0:  successful exit */
/*          < 0:  if INFO = -i, the i-th argument had an illegal value. */
/*          = 1,...,N: */
/*                The QZ iteration failed.  No eigenvectors have been */
/*                calculated, but ALPHAR(j), ALPHAI(j), and BETA(j) */
/*                should be correct for j=INFO+1,...,N. */
/*          > N:  errors that usually indicate LAPACK problems: */
/*                =N+1: error return from SGGBAL */
/*                =N+2: error return from SGEQRF */
/*                =N+3: error return from SORMQR */
/*                =N+4: error return from SORGQR */
/*                =N+5: error return from SGGHRD */
/*                =N+6: error return from SHGEQZ (other than failed */
/*                                                iteration) */
/*                =N+7: error return from STGEVC */
/*                =N+8: error return from SGGBAK (computing VL) */
/*                =N+9: error return from SGGBAK (computing VR) */
/*                =N+10: error return from SLASCL (various calls) */

/*  Further Details */
/*  =============== */

/*  Balancing */
/*  --------- */

/*  This driver calls SGGBAL to both permute and scale rows and columns */
/*  of A and B.  The permutations PL and PR are chosen so that PL*A*PR */
/*  and PL*B*R will be upper triangular except for the diagonal blocks */
/*  A(i:j,i:j) and B(i:j,i:j), with i and j as close together as */
/*  possible.  The diagonal scaling matrices DL and DR are chosen so */
/*  that the pair  DL*PL*A*PR*DR, DL*PL*B*PR*DR have elements close to */
/*  one (except for the elements that start out zero.) */

/*  After the eigenvalues and eigenvectors of the balanced matrices */
/*  have been computed, SGGBAK transforms the eigenvectors back to what */
/*  they would have been (in perfect arithmetic) if they had not been */
/*  balanced. */

/*  Contents of A and B on Exit */
/*  -------- -- - --- - -- ---- */

/*  If any eigenvectors are computed (either JOBVL='V' or JOBVR='V' or */
/*  both), then on exit the arrays A and B will contain the real Schur */
/*  form[*] of the "balanced" versions of A and B.  If no eigenvectors */
/*  are computed, then only the diagonal blocks will be correct. */

/*  [*] See SHGEQZ, SGEGS, or read the book "Matrix Computations", */
/*      by Golub & van Loan, pub. by Johns Hopkins U. Press. */

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

/*     .. 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;
    --work;

    /* 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;

/*     Test the input arguments */

/* Computing MAX */
    i__1 = *n << 3;
    lwkmin = max(i__1,1);
    lwkopt = lwkmin;
    work[1] = (real) lwkopt;
    lquery = *lwork == -1;
    *info = 0;
    if (ijobvl <= 0) {
        *info = -1;
    } else if (ijobvr <= 0) {
        *info = -2;
    } else if (*n < 0) {
        *info = -3;
    } else if (*lda < max(1,*n)) {
        *info = -5;
    } else if (*ldb < max(1,*n)) {
        *info = -7;
    } else if (*ldvl < 1 || ilvl && *ldvl < *n) {
        *info = -12;
    } else if (*ldvr < 1 || ilvr && *ldvr < *n) {
        *info = -14;
    } else if (*lwork < lwkmin && ! lquery) {
        *info = -16;
    }

    if (*info == 0) {
        nb1 = ilaenv_(&c__1, "SGEQRF", " ", n, n, &c_n1, &c_n1);
        nb2 = ilaenv_(&c__1, "SORMQR", " ", n, n, n, &c_n1);
        nb3 = ilaenv_(&c__1, "SORGQR", " ", n, n, n, &c_n1);
/* Computing MAX */
        i__1 = max(nb1,nb2);
        nb = max(i__1,nb3);
/* Computing MAX */
        i__1 = *n * 6, i__2 = *n * (nb + 1);
        lopt = (*n << 1) + max(i__1,i__2);
        work[1] = (real) lopt;
    }

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

/*     Quick return if possible */

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

/*     Get machine constants */

    eps = slamch_("E") * slamch_("B");
    safmin = slamch_("S");
    safmin += safmin;
    safmax = 1.f / safmin;
    onepls = eps * 4 + 1.f;

/*     Scale A */

    anrm = slange_("M", n, n, &a[a_offset], lda, &work[1]);
    anrm1 = anrm;
    anrm2 = 1.f;
    if (anrm < 1.f) {
        if (safmax * anrm < 1.f) {
            anrm1 = safmin;
            anrm2 = safmax * anrm;
        }
    }

    if (anrm > 0.f) {
        slascl_("G", &c_n1, &c_n1, &anrm, &c_b27, n, n, &a[a_offset], lda, &
                iinfo);
        if (iinfo != 0) {
            *info = *n + 10;
            return 0;
        }
    }

/*     Scale B */

    bnrm = slange_("M", n, n, &b[b_offset], ldb, &work[1]);
    bnrm1 = bnrm;
    bnrm2 = 1.f;
    if (bnrm < 1.f) {
        if (safmax * bnrm < 1.f) {
            bnrm1 = safmin;
            bnrm2 = safmax * bnrm;
        }
    }

    if (bnrm > 0.f) {
        slascl_("G", &c_n1, &c_n1, &bnrm, &c_b27, n, n, &b[b_offset], ldb, &
                iinfo);
        if (iinfo != 0) {
            *info = *n + 10;
            return 0;
        }
    }

/*     Permute the matrix to make it more nearly triangular */
/*     Workspace layout:  (8*N words -- "work" requires 6*N words) */
/*        left_permutation, right_permutation, work... */

    ileft = 1;
    iright = *n + 1;
    iwork = iright + *n;
    sggbal_("P", n, &a[a_offset], lda, &b[b_offset], ldb, &ilo, &ihi, &work[
            ileft], &work[iright], &work[iwork], &iinfo);
    if (iinfo != 0) {
        *info = *n + 1;
        goto L120;
    }

/*     Reduce B to triangular form, and initialize VL and/or VR */
/*     Workspace layout:  ("work..." must have at least N words) */
/*        left_permutation, right_permutation, tau, work... */

    irows = ihi + 1 - ilo;
    if (ilv) {
        icols = *n + 1 - ilo;
    } else {
        icols = irows;
    }
    itau = iwork;
    iwork = itau + irows;
    i__1 = *lwork + 1 - iwork;
    sgeqrf_(&irows, &icols, &b[ilo + ilo * b_dim1], ldb, &work[itau], &work[
            iwork], &i__1, &iinfo);
    if (iinfo >= 0) {
/* Computing MAX */
        i__1 = lwkopt, i__2 = (integer) work[iwork] + iwork - 1;
        lwkopt = max(i__1,i__2);
    }
    if (iinfo != 0) {
        *info = *n + 2;
        goto L120;
    }

    i__1 = *lwork + 1 - iwork;
    sormqr_("L", "T", &irows, &icols, &irows, &b[ilo + ilo * b_dim1], ldb, &
            work[itau], &a[ilo + ilo * a_dim1], lda, &work[iwork], &i__1, &
            iinfo);
    if (iinfo >= 0) {
/* Computing MAX */
        i__1 = lwkopt, i__2 = (integer) work[iwork] + iwork - 1;
        lwkopt = max(i__1,i__2);
    }
    if (iinfo != 0) {
        *info = *n + 3;
        goto L120;
    }

    if (ilvl) {
        slaset_("Full", n, n, &c_b38, &c_b27, &vl[vl_offset], ldvl)
                ;
        i__1 = irows - 1;
        i__2 = irows - 1;
        slacpy_("L", &i__1, &i__2, &b[ilo + 1 + ilo * b_dim1], ldb, &vl[ilo + 
                1 + ilo * vl_dim1], ldvl);
        i__1 = *lwork + 1 - iwork;
        sorgqr_(&irows, &irows, &irows, &vl[ilo + ilo * vl_dim1], ldvl, &work[
                itau], &work[iwork], &i__1, &iinfo);
        if (iinfo >= 0) {
/* Computing MAX */
            i__1 = lwkopt, i__2 = (integer) work[iwork] + iwork - 1;
            lwkopt = max(i__1,i__2);
        }
        if (iinfo != 0) {
            *info = *n + 4;
            goto L120;
        }
    }

    if (ilvr) {
        slaset_("Full", n, n, &c_b38, &c_b27, &vr[vr_offset], ldvr)
                ;
    }

/*     Reduce to generalized Hessenberg form */

    if (ilv) {

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

        sgghrd_(jobvl, jobvr, n, &ilo, &ihi, &a[a_offset], lda, &b[b_offset], 
                ldb, &vl[vl_offset], ldvl, &vr[vr_offset], ldvr, &iinfo);
    } else {
        sgghrd_("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, &iinfo);
    }
    if (iinfo != 0) {
        *info = *n + 5;
        goto L120;
    }

/*     Perform QZ algorithm */
/*     Workspace layout:  ("work..." must have at least 1 word) */
/*        left_permutation, right_permutation, work... */

    iwork = itau;
    if (ilv) {
        *(unsigned char *)chtemp = 'S';
    } else {
        *(unsigned char *)chtemp = 'E';
    }
    i__1 = *lwork + 1 - iwork;
    shgeqz_(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[iwork], &i__1, &iinfo);
    if (iinfo >= 0) {
/* Computing MAX */
        i__1 = lwkopt, i__2 = (integer) work[iwork] + iwork - 1;
        lwkopt = max(i__1,i__2);
    }
    if (iinfo != 0) {
        if (iinfo > 0 && iinfo <= *n) {
            *info = iinfo;
        } else if (iinfo > *n && iinfo <= *n << 1) {
            *info = iinfo - *n;
        } else {
            *info = *n + 6;
        }
        goto L120;
    }

    if (ilv) {

/*        Compute Eigenvectors  (STGEVC requires 6*N words of workspace) */

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

        stgevc_(chtemp, "B", ldumma, n, &a[a_offset], lda, &b[b_offset], ldb, 
                &vl[vl_offset], ldvl, &vr[vr_offset], ldvr, n, &in, &work[
                iwork], &iinfo);
        if (iinfo != 0) {
            *info = *n + 7;
            goto L120;
        }

/*        Undo balancing on VL and VR, rescale */

        if (ilvl) {
            sggbak_("P", "L", n, &ilo, &ihi, &work[ileft], &work[iright], n, &
                    vl[vl_offset], ldvl, &iinfo);
            if (iinfo != 0) {
                *info = *n + 8;
                goto L120;
            }
            i__1 = *n;
            for (jc = 1; jc <= i__1; ++jc) {
                if (alphai[jc] < 0.f) {
                    goto L50;
                }
                temp = 0.f;
                if (alphai[jc] == 0.f) {
                    i__2 = *n;
                    for (jr = 1; jr <= i__2; ++jr) {
/* Computing MAX */
                        r__2 = temp, r__3 = (r__1 = vl[jr + jc * vl_dim1], 
                                dabs(r__1));
                        temp = dmax(r__2,r__3);
/* L10: */
                    }
                } else {
                    i__2 = *n;
                    for (jr = 1; jr <= i__2; ++jr) {
/* Computing MAX */
                        r__3 = temp, r__4 = (r__1 = vl[jr + jc * vl_dim1], 
                                dabs(r__1)) + (r__2 = vl[jr + (jc + 1) * 
                                vl_dim1], dabs(r__2));
                        temp = dmax(r__3,r__4);
/* L20: */
                    }
                }
                if (temp < safmin) {
                    goto L50;
                }
                temp = 1.f / temp;
                if (alphai[jc] == 0.f) {
                    i__2 = *n;
                    for (jr = 1; jr <= i__2; ++jr) {
                        vl[jr + jc * vl_dim1] *= temp;
/* L30: */
                    }
                } else {
                    i__2 = *n;
                    for (jr = 1; jr <= i__2; ++jr) {
                        vl[jr + jc * vl_dim1] *= temp;
                        vl[jr + (jc + 1) * vl_dim1] *= temp;
/* L40: */
                    }
                }
L50:
                ;
            }
        }
        if (ilvr) {
            sggbak_("P", "R", n, &ilo, &ihi, &work[ileft], &work[iright], n, &
                    vr[vr_offset], ldvr, &iinfo);
            if (iinfo != 0) {
                *info = *n + 9;
                goto L120;
            }
            i__1 = *n;
            for (jc = 1; jc <= i__1; ++jc) {
                if (alphai[jc] < 0.f) {
                    goto L100;
                }
                temp = 0.f;
                if (alphai[jc] == 0.f) {
                    i__2 = *n;
                    for (jr = 1; jr <= i__2; ++jr) {
/* Computing MAX */
                        r__2 = temp, r__3 = (r__1 = vr[jr + jc * vr_dim1], 
                                dabs(r__1));
                        temp = dmax(r__2,r__3);
/* L60: */
                    }
                } else {
                    i__2 = *n;
                    for (jr = 1; jr <= i__2; ++jr) {
/* Computing MAX */
                        r__3 = temp, r__4 = (r__1 = vr[jr + jc * vr_dim1], 
                                dabs(r__1)) + (r__2 = vr[jr + (jc + 1) * 
                                vr_dim1], dabs(r__2));
                        temp = dmax(r__3,r__4);
/* L70: */
                    }
                }
                if (temp < safmin) {
                    goto L100;
                }
                temp = 1.f / temp;
                if (alphai[jc] == 0.f) {
                    i__2 = *n;
                    for (jr = 1; jr <= i__2; ++jr) {
                        vr[jr + jc * vr_dim1] *= temp;
/* L80: */
                    }
                } else {
                    i__2 = *n;
                    for (jr = 1; jr <= i__2; ++jr) {
                        vr[jr + jc * vr_dim1] *= temp;
                        vr[jr + (jc + 1) * vr_dim1] *= temp;
/* L90: */
                    }
                }
L100:
                ;
            }
        }

/*        End of eigenvector calculation */

    }

/*     Undo scaling in alpha, beta */

/*     Note: this does not give the alpha and beta for the unscaled */
/*     problem. */

/*     Un-scaling is limited to avoid underflow in alpha and beta */
/*     if they are significant. */

    i__1 = *n;
    for (jc = 1; jc <= i__1; ++jc) {
        absar = (r__1 = alphar[jc], dabs(r__1));
        absai = (r__1 = alphai[jc], dabs(r__1));
        absb = (r__1 = beta[jc], dabs(r__1));
        salfar = anrm * alphar[jc];
        salfai = anrm * alphai[jc];
        sbeta = bnrm * beta[jc];
        ilimit = FALSE_;
        scale = 1.f;

/*        Check for significant underflow in ALPHAI */

/* Computing MAX */
        r__1 = safmin, r__2 = eps * absar, r__1 = max(r__1,r__2), r__2 = eps *
                 absb;
        if (dabs(salfai) < safmin && absai >= dmax(r__1,r__2)) {
            ilimit = TRUE_;
/* Computing MAX */
            r__1 = onepls * safmin, r__2 = anrm2 * absai;
            scale = onepls * safmin / anrm1 / dmax(r__1,r__2);

        } else if (salfai == 0.f) {

/*           If insignificant underflow in ALPHAI, then make the */
/*           conjugate eigenvalue real. */

            if (alphai[jc] < 0.f && jc > 1) {
                alphai[jc - 1] = 0.f;
            } else if (alphai[jc] > 0.f && jc < *n) {
                alphai[jc + 1] = 0.f;
            }
        }

/*        Check for significant underflow in ALPHAR */

/* Computing MAX */
        r__1 = safmin, r__2 = eps * absai, r__1 = max(r__1,r__2), r__2 = eps *
                 absb;
        if (dabs(salfar) < safmin && absar >= dmax(r__1,r__2)) {
            ilimit = TRUE_;
/* Computing MAX */
/* Computing MAX */
            r__3 = onepls * safmin, r__4 = anrm2 * absar;
            r__1 = scale, r__2 = onepls * safmin / anrm1 / dmax(r__3,r__4);
            scale = dmax(r__1,r__2);
        }

/*        Check for significant underflow in BETA */

/* Computing MAX */
        r__1 = safmin, r__2 = eps * absar, r__1 = max(r__1,r__2), r__2 = eps *
                 absai;
        if (dabs(sbeta) < safmin && absb >= dmax(r__1,r__2)) {
            ilimit = TRUE_;
/* Computing MAX */
/* Computing MAX */
            r__3 = onepls * safmin, r__4 = bnrm2 * absb;
            r__1 = scale, r__2 = onepls * safmin / bnrm1 / dmax(r__3,r__4);
            scale = dmax(r__1,r__2);
        }

/*        Check for possible overflow when limiting scaling */

        if (ilimit) {
/* Computing MAX */
            r__1 = dabs(salfar), r__2 = dabs(salfai), r__1 = max(r__1,r__2), 
                    r__2 = dabs(sbeta);
            temp = scale * safmin * dmax(r__1,r__2);
            if (temp > 1.f) {
                scale /= temp;
            }
            if (scale < 1.f) {
                ilimit = FALSE_;
            }
        }

/*        Recompute un-scaled ALPHAR, ALPHAI, BETA if necessary. */

        if (ilimit) {
            salfar = scale * alphar[jc] * anrm;
            salfai = scale * alphai[jc] * anrm;
            sbeta = scale * beta[jc] * bnrm;
        }
        alphar[jc] = salfar;
        alphai[jc] = salfai;
        beta[jc] = sbeta;
/* L110: */
    }

L120:
    work[1] = (real) lwkopt;

    return 0;

/*     End of SGEGV */

} /* sgegv_ */