/* ./src_f77/zgegs.f -- translated by f2c (version 20030320).
   You must link the resulting object file with the libraries:
	-lf2c -lm   (in that order)
*/

#include <punc/vf2c.h>

/* Table of constant values */

static doublecomplex c_b1 = {0.,0.};
static doublecomplex c_b2 = {1.,0.};
static integer c__1 = 1;
static integer c_n1 = -1;

/* Subroutine */ int zgegs_(char *jobvsl, char *jobvsr, integer *n, 
	doublecomplex *a, integer *lda, doublecomplex *b, integer *ldb, 
	doublecomplex *alpha, doublecomplex *beta, doublecomplex *vsl, 
	integer *ldvsl, doublecomplex *vsr, integer *ldvsr, doublecomplex *
	work, integer *lwork, doublereal *rwork, integer *info, ftnlen 
	jobvsl_len, ftnlen jobvsr_len)
{
    /* System generated locals */
    integer a_dim1, a_offset, b_dim1, b_offset, vsl_dim1, vsl_offset, 
	    vsr_dim1, vsr_offset, i__1, i__2, i__3;

    /* Local variables */
    static integer nb, nb1, nb2, nb3, ihi, ilo;
    static doublereal eps, anrm, bnrm;
    static integer itau, lopt;
    extern logical lsame_(char *, char *, ftnlen, ftnlen);
    static integer ileft, iinfo, icols;
    static logical ilvsl;
    static integer iwork;
    static logical ilvsr;
    static integer irows;
    extern doublereal dlamch_(char *, ftnlen);
    extern /* Subroutine */ int zggbak_(char *, char *, integer *, integer *, 
	    integer *, doublereal *, doublereal *, integer *, doublecomplex *,
	     integer *, integer *, ftnlen, ftnlen), zggbal_(char *, integer *,
	     doublecomplex *, integer *, doublecomplex *, integer *, integer *
	    , integer *, doublereal *, doublereal *, doublereal *, integer *, 
	    ftnlen);
    static logical ilascl, ilbscl;
    static doublereal safmin;
    extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
    extern integer ilaenv_(integer *, char *, char *, integer *, integer *, 
	    integer *, integer *, ftnlen, ftnlen);
    extern doublereal zlange_(char *, integer *, integer *, doublecomplex *, 
	    integer *, doublereal *, ftnlen);
    static doublereal bignum;
    static integer ijobvl, iright;
    extern /* Subroutine */ int zgghrd_(char *, char *, integer *, integer *, 
	    integer *, doublecomplex *, integer *, doublecomplex *, integer *,
	     doublecomplex *, integer *, doublecomplex *, integer *, integer *
	    , ftnlen, ftnlen), zlascl_(char *, integer *, integer *, 
	    doublereal *, doublereal *, integer *, integer *, doublecomplex *,
	     integer *, integer *, ftnlen);
    static integer ijobvr;
    extern /* Subroutine */ int zgeqrf_(integer *, integer *, doublecomplex *,
	     integer *, doublecomplex *, doublecomplex *, integer *, integer *
	    );
    static doublereal anrmto;
    static integer lwkmin;
    static doublereal bnrmto;
    extern /* Subroutine */ int zlacpy_(char *, integer *, integer *, 
	    doublecomplex *, integer *, doublecomplex *, integer *, ftnlen), 
	    zlaset_(char *, integer *, integer *, doublecomplex *, 
	    doublecomplex *, doublecomplex *, integer *, ftnlen), zhgeqz_(
	    char *, char *, char *, integer *, integer *, integer *, 
	    doublecomplex *, integer *, doublecomplex *, integer *, 
	    doublecomplex *, doublecomplex *, doublecomplex *, integer *, 
	    doublecomplex *, integer *, doublecomplex *, integer *, 
	    doublereal *, integer *, ftnlen, ftnlen, ftnlen);
    static doublereal smlnum;
    static integer irwork, lwkopt;
    static logical lquery;
    extern /* Subroutine */ int zungqr_(integer *, integer *, integer *, 
	    doublecomplex *, integer *, doublecomplex *, doublecomplex *, 
	    integer *, integer *), zunmqr_(char *, char *, integer *, integer 
	    *, integer *, doublecomplex *, integer *, doublecomplex *, 
	    doublecomplex *, integer *, doublecomplex *, integer *, integer *,
	     ftnlen, ftnlen);


/*  -- 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 */

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

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

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

/*  ZGEGS computes for a pair of N-by-N complex nonsymmetric matrices A, */
/*  B:  the generalized eigenvalues (alpha, beta), the complex Schur */
/*  form (A, B), and optionally left and/or right Schur vectors */
/*  (VSL and VSR). */

/*  (If only the generalized eigenvalues are needed, use the driver ZGEGV */
/*  instead.) */

/*  A generalized eigenvalue for a pair of matrices (A,B) is, roughly */
/*  speaking, 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, and even for */
/*  both being zero.  A good beginning reference is the book, "Matrix */
/*  Computations", by G. Golub & C. van Loan (Johns Hopkins U. Press) */

/*  The (generalized) Schur form of a pair of matrices is the result of */
/*  multiplying both matrices on the left by one unitary matrix and */
/*  both on the right by another unitary matrix, these two unitary */
/*  matrices being chosen so as to bring the pair of matrices into */
/*  upper triangular form with the diagonal elements of B being */
/*  non-negative real numbers (this is also called complex Schur form.) */

/*  The left and right Schur vectors are the columns of VSL and VSR, */
/*  respectively, where VSL and VSR are the unitary matrices */
/*  which reduce A and B to Schur form: */

/*  Schur form of (A,B) = ( (VSL)**H A (VSR), (VSL)**H B (VSR) ) */

/*  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. */

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

/*  A       (input/output) COMPLEX*16 array, dimension (LDA, N) */
/*          On entry, the first of the pair of matrices whose generalized */
/*          eigenvalues and (optionally) Schur vectors are to be */
/*          computed. */
/*          On exit, the generalized Schur form of A. */

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

/*  B       (input/output) COMPLEX*16 array, dimension (LDB, N) */
/*          On entry, the second of the pair of matrices whose */
/*          generalized eigenvalues and (optionally) Schur vectors are */
/*          to be computed. */
/*          On exit, the generalized Schur form of B. */

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

/*  ALPHA   (output) COMPLEX*16 array, dimension (N) */
/*  BETA    (output) COMPLEX*16 array, dimension (N) */
/*          On exit,  ALPHA(j)/BETA(j), j=1,...,N, will be the */
/*          generalized eigenvalues.  ALPHA(j), j=1,...,N  and  BETA(j), */
/*          j=1,...,N  are the diagonals of the complex Schur form (A,B) */
/*          output by ZGEGS.  The  BETA(j) will be non-negative real. */

/*          Note: the quotients ALPHA(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, ALPHA 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) COMPLEX*16 array, dimension (LDVSL,N) */
/*          If JOBVSL = 'V', VSL will contain the left Schur vectors. */
/*          (See "Purpose", above.) */
/*          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) COMPLEX*16 array, dimension (LDVSR,N) */
/*          If JOBVSR = 'V', VSR will contain the right Schur vectors. */
/*          (See "Purpose", above.) */
/*          Not referenced if JOBVSR = 'N'. */

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

/*  WORK    (workspace/output) COMPLEX*16 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(1,2*N). */
/*          For good performance, LWORK must generally be larger. */
/*          To compute the optimal value of LWORK, call ILAENV to get */
/*          blocksizes (for ZGEQRF, ZUNMQR, and CUNGQR.)  Then compute: */
/*          NB  -- MAX of the blocksizes for ZGEQRF, ZUNMQR, and CUNGQR; */
/*          the optimal LWORK is 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. */

/*  RWORK   (workspace) DOUBLE PRECISION array, dimension (3*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 ALPHA(j) and BETA(j) should be correct for */
/*                j=INFO+1,...,N. */
/*          > N:  errors that usually indicate LAPACK problems: */
/*                =N+1: error return from ZGGBAL */
/*                =N+2: error return from ZGEQRF */
/*                =N+3: error return from ZUNMQR */
/*                =N+4: error return from ZUNGQR */
/*                =N+5: error return from ZGGHRD */
/*                =N+6: error return from ZHGEQZ (other than failed */
/*                                               iteration) */
/*                =N+7: error return from ZGGBAK (computing VSL) */
/*                =N+8: error return from ZGGBAK (computing VSR) */
/*                =N+9: error return from ZLASCL (various places) */

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

/*     .. Parameters .. */
/*     .. */
/*     .. Local Scalars .. */
/*     .. */
/*     .. 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;
    --alpha;
    --beta;
    vsl_dim1 = *ldvsl;
    vsl_offset = 1 + vsl_dim1;
    vsl -= vsl_offset;
    vsr_dim1 = *ldvsr;
    vsr_offset = 1 + vsr_dim1;
    vsr -= vsr_offset;
    --work;
    --rwork;

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

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

/*     Test the input arguments */

/* Computing MAX */
    i__1 = *n << 1;
    lwkmin = max(i__1,1);
    lwkopt = lwkmin;
    work[1].r = (doublereal) lwkopt, work[1].i = 0.;
    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 (*ldvsl < 1 || ilvsl && *ldvsl < *n) {
	*info = -11;
    } else if (*ldvsr < 1 || ilvsr && *ldvsr < *n) {
	*info = -13;
    } else if (*lwork < lwkmin && ! lquery) {
	*info = -15;
    }

    if (*info == 0) {
	nb1 = ilaenv_(&c__1, "ZGEQRF", " ", n, n, &c_n1, &c_n1, (ftnlen)6, (
		ftnlen)1);
	nb2 = ilaenv_(&c__1, "ZUNMQR", " ", n, n, n, &c_n1, (ftnlen)6, (
		ftnlen)1);
	nb3 = ilaenv_(&c__1, "ZUNGQR", " ", n, n, n, &c_n1, (ftnlen)6, (
		ftnlen)1);
/* Computing MAX */
	i__1 = max(nb1,nb2);
	nb = max(i__1,nb3);
	lopt = *n * (nb + 1);
	work[1].r = (doublereal) lopt, work[1].i = 0.;
    }

    if (*info != 0) {
	i__1 = -(*info);
	xerbla_("ZGEGS ", &i__1, (ftnlen)6);
	return 0;
    } else if (lquery) {
	return 0;
    }

/*     Quick return if possible */

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

/*     Get machine constants */

    eps = dlamch_("E", (ftnlen)1) * dlamch_("B", (ftnlen)1);
    safmin = dlamch_("S", (ftnlen)1);
    smlnum = *n * safmin / eps;
    bignum = 1. / smlnum;

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

    anrm = zlange_("M", n, n, &a[a_offset], lda, &rwork[1], (ftnlen)1);
    ilascl = FALSE_;
    if (anrm > 0. && anrm < smlnum) {
	anrmto = smlnum;
	ilascl = TRUE_;
    } else if (anrm > bignum) {
	anrmto = bignum;
	ilascl = TRUE_;
    }

    if (ilascl) {
	zlascl_("G", &c_n1, &c_n1, &anrm, &anrmto, n, n, &a[a_offset], lda, &
		iinfo, (ftnlen)1);
	if (iinfo != 0) {
	    *info = *n + 9;
	    return 0;
	}
    }

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

    bnrm = zlange_("M", n, n, &b[b_offset], ldb, &rwork[1], (ftnlen)1);
    ilbscl = FALSE_;
    if (bnrm > 0. && bnrm < smlnum) {
	bnrmto = smlnum;
	ilbscl = TRUE_;
    } else if (bnrm > bignum) {
	bnrmto = bignum;
	ilbscl = TRUE_;
    }

    if (ilbscl) {
	zlascl_("G", &c_n1, &c_n1, &bnrm, &bnrmto, n, n, &b[b_offset], ldb, &
		iinfo, (ftnlen)1);
	if (iinfo != 0) {
	    *info = *n + 9;
	    return 0;
	}
    }

/*     Permute the matrix to make it more nearly triangular */

    ileft = 1;
    iright = *n + 1;
    irwork = iright + *n;
    iwork = 1;
    zggbal_("P", n, &a[a_offset], lda, &b[b_offset], ldb, &ilo, &ihi, &rwork[
	    ileft], &rwork[iright], &rwork[irwork], &iinfo, (ftnlen)1);
    if (iinfo != 0) {
	*info = *n + 1;
	goto L10;
    }

/*     Reduce B to triangular form, and initialize VSL and/or VSR */

    irows = ihi + 1 - ilo;
    icols = *n + 1 - ilo;
    itau = iwork;
    iwork = itau + irows;
    i__1 = *lwork + 1 - iwork;
    zgeqrf_(&irows, &icols, &b[ilo + ilo * b_dim1], ldb, &work[itau], &work[
	    iwork], &i__1, &iinfo);
    if (iinfo >= 0) {
/* Computing MAX */
	i__3 = iwork;
	i__1 = lwkopt, i__2 = (integer) work[i__3].r + iwork - 1;
	lwkopt = max(i__1,i__2);
    }
    if (iinfo != 0) {
	*info = *n + 2;
	goto L10;
    }

    i__1 = *lwork + 1 - iwork;
    zunmqr_("L", "C", &irows, &icols, &irows, &b[ilo + ilo * b_dim1], ldb, &
	    work[itau], &a[ilo + ilo * a_dim1], lda, &work[iwork], &i__1, &
	    iinfo, (ftnlen)1, (ftnlen)1);
    if (iinfo >= 0) {
/* Computing MAX */
	i__3 = iwork;
	i__1 = lwkopt, i__2 = (integer) work[i__3].r + iwork - 1;
	lwkopt = max(i__1,i__2);
    }
    if (iinfo != 0) {
	*info = *n + 3;
	goto L10;
    }

    if (ilvsl) {
	zlaset_("Full", n, n, &c_b1, &c_b2, &vsl[vsl_offset], ldvsl, (ftnlen)
		4);
	i__1 = irows - 1;
	i__2 = irows - 1;
	zlacpy_("L", &i__1, &i__2, &b[ilo + 1 + ilo * b_dim1], ldb, &vsl[ilo 
		+ 1 + ilo * vsl_dim1], ldvsl, (ftnlen)1);
	i__1 = *lwork + 1 - iwork;
	zungqr_(&irows, &irows, &irows, &vsl[ilo + ilo * vsl_dim1], ldvsl, &
		work[itau], &work[iwork], &i__1, &iinfo);
	if (iinfo >= 0) {
/* Computing MAX */
	    i__3 = iwork;
	    i__1 = lwkopt, i__2 = (integer) work[i__3].r + iwork - 1;
	    lwkopt = max(i__1,i__2);
	}
	if (iinfo != 0) {
	    *info = *n + 4;
	    goto L10;
	}
    }

    if (ilvsr) {
	zlaset_("Full", n, n, &c_b1, &c_b2, &vsr[vsr_offset], ldvsr, (ftnlen)
		4);
    }

/*     Reduce to generalized Hessenberg form */

    zgghrd_(jobvsl, jobvsr, n, &ilo, &ihi, &a[a_offset], lda, &b[b_offset], 
	    ldb, &vsl[vsl_offset], ldvsl, &vsr[vsr_offset], ldvsr, &iinfo, (
	    ftnlen)1, (ftnlen)1);
    if (iinfo != 0) {
	*info = *n + 5;
	goto L10;
    }

/*     Perform QZ algorithm, computing Schur vectors if desired */

    iwork = itau;
    i__1 = *lwork + 1 - iwork;
    zhgeqz_("S", jobvsl, jobvsr, n, &ilo, &ihi, &a[a_offset], lda, &b[
	    b_offset], ldb, &alpha[1], &beta[1], &vsl[vsl_offset], ldvsl, &
	    vsr[vsr_offset], ldvsr, &work[iwork], &i__1, &rwork[irwork], &
	    iinfo, (ftnlen)1, (ftnlen)1, (ftnlen)1);
    if (iinfo >= 0) {
/* Computing MAX */
	i__3 = iwork;
	i__1 = lwkopt, i__2 = (integer) work[i__3].r + 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 L10;
    }

/*     Apply permutation to VSL and VSR */

    if (ilvsl) {
	zggbak_("P", "L", n, &ilo, &ihi, &rwork[ileft], &rwork[iright], n, &
		vsl[vsl_offset], ldvsl, &iinfo, (ftnlen)1, (ftnlen)1);
	if (iinfo != 0) {
	    *info = *n + 7;
	    goto L10;
	}
    }
    if (ilvsr) {
	zggbak_("P", "R", n, &ilo, &ihi, &rwork[ileft], &rwork[iright], n, &
		vsr[vsr_offset], ldvsr, &iinfo, (ftnlen)1, (ftnlen)1);
	if (iinfo != 0) {
	    *info = *n + 8;
	    goto L10;
	}
    }

/*     Undo scaling */

    if (ilascl) {
	zlascl_("U", &c_n1, &c_n1, &anrmto, &anrm, n, n, &a[a_offset], lda, &
		iinfo, (ftnlen)1);
	if (iinfo != 0) {
	    *info = *n + 9;
	    return 0;
	}
	zlascl_("G", &c_n1, &c_n1, &anrmto, &anrm, n, &c__1, &alpha[1], n, &
		iinfo, (ftnlen)1);
	if (iinfo != 0) {
	    *info = *n + 9;
	    return 0;
	}
    }

    if (ilbscl) {
	zlascl_("U", &c_n1, &c_n1, &bnrmto, &bnrm, n, n, &b[b_offset], ldb, &
		iinfo, (ftnlen)1);
	if (iinfo != 0) {
	    *info = *n + 9;
	    return 0;
	}
	zlascl_("G", &c_n1, &c_n1, &bnrmto, &bnrm, n, &c__1, &beta[1], n, &
		iinfo, (ftnlen)1);
	if (iinfo != 0) {
	    *info = *n + 9;
	    return 0;
	}
    }

L10:
    work[1].r = (doublereal) lwkopt, work[1].i = 0.;

    return 0;

/*     End of ZGEGS */

} /* zgegs_ */

