/* ./src_f77/sgegs.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 integer c__1 = 1;
static integer c_n1 = -1;
static real c_b36 = 0.f;
static real c_b37 = 1.f;

/* Subroutine */ int sgegs_(char *jobvsl, char *jobvsr, integer *n, real *a, 
	integer *lda, real *b, integer *ldb, real *alphar, real *alphai, real 
	*beta, real *vsl, integer *ldvsl, real *vsr, integer *ldvsr, real *
	work, integer *lwork, 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;

    /* Local variables */
    static integer nb, nb1, nb2, nb3, ihi, ilo;
    static real 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 /* Subroutine */ int sggbak_(char *, char *, integer *, integer *, 
	    integer *, real *, real *, integer *, real *, integer *, integer *
	    , ftnlen, ftnlen), sggbal_(char *, integer *, real *, integer *, 
	    real *, integer *, integer *, integer *, real *, real *, real *, 
	    integer *, ftnlen);
    static logical ilascl, ilbscl;
    extern doublereal slamch_(char *, ftnlen), slange_(char *, integer *, 
	    integer *, real *, integer *, real *, ftnlen);
    static real safmin;
    extern /* Subroutine */ int sgghrd_(char *, char *, integer *, integer *, 
	    integer *, real *, integer *, real *, integer *, real *, integer *
	    , real *, integer *, integer *, ftnlen, ftnlen), xerbla_(char *, 
	    integer *, ftnlen);
    extern integer ilaenv_(integer *, char *, char *, integer *, integer *, 
	    integer *, integer *, ftnlen, ftnlen);
    static real bignum;
    extern /* Subroutine */ int slascl_(char *, integer *, integer *, real *, 
	    real *, integer *, integer *, real *, integer *, integer *, 
	    ftnlen);
    static integer ijobvl, iright;
    extern /* Subroutine */ int sgeqrf_(integer *, integer *, real *, integer 
	    *, real *, real *, integer *, integer *);
    static integer ijobvr;
    extern /* Subroutine */ int slacpy_(char *, integer *, integer *, real *, 
	    integer *, real *, integer *, ftnlen), slaset_(char *, integer *, 
	    integer *, real *, real *, real *, integer *, ftnlen);
    static real anrmto;
    static integer lwkmin;
    static real bnrmto;
    extern /* Subroutine */ int shgeqz_(char *, char *, char *, integer *, 
	    integer *, integer *, real *, integer *, real *, integer *, real *
	    , real *, real *, real *, integer *, real *, integer *, real *, 
	    integer *, integer *, ftnlen, ftnlen, ftnlen);
    static real smlnum;
    extern /* Subroutine */ int sorgqr_(integer *, integer *, integer *, real 
	    *, integer *, real *, real *, integer *, integer *);
    static integer lwkopt;
    static logical lquery;
    extern /* Subroutine */ int sormqr_(char *, char *, integer *, integer *, 
	    integer *, real *, integer *, real *, real *, integer *, real *, 
	    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 SGGES. */

/*  SGEGS computes for a pair of N-by-N real nonsymmetric matrices A, B: */
/*  the generalized eigenvalues (alphar +/- alphai*i, beta), the real */
/*  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 SGEGV */
/*  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 orthogonal matrix and */
/*  both on the right by another orthogonal matrix, these two orthogonal */
/*  matrices being chosen so as to bring the pair of matrices into */
/*  (real) Schur form. */

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

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

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

/*  Schur form of (A,B) = ( (VSL)**T A (VSR), (VSL)**T 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) REAL 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. */
/*          Note: to avoid overflow, the Frobenius norm of the matrix */
/*          A should be less than the overflow threshold. */

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

/*  B       (input/output) REAL 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. */
/*          Note: to avoid overflow, the Frobenius norm of the matrix */
/*          B should be less than the overflow threshold. */

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

/*  ALPHAR  (output) REAL array, dimension (N) */
/*  ALPHAI  (output) REAL array, dimension (N) */
/*  BETA    (output) REAL array, dimension (N) */
/*          On exit, (ALPHAR(j) + ALPHAI(j)*i)/BETA(j), j=1,...,N, will */
/*          be the generalized eigenvalues.  ALPHAR(j) + ALPHAI(j)*i, */
/*          j=1,...,N  and  BETA(j),j=1,...,N  are the diagonals of the */
/*          complex Schur form (A,B) that would result if the 2-by-2 */
/*          diagonal blocks of the real Schur form of (A,B) were further */
/*          reduced to triangular form using 2-by-2 complex unitary */
/*          transformations.  If ALPHAI(j) is zero, then the j-th */
/*          eigenvalue is real; if positive, then the j-th and (j+1)-st */
/*          eigenvalues are a complex conjugate pair, with ALPHAI(j+1) */
/*          negative. */

/*          Note: the quotients ALPHAR(j)/BETA(j) and ALPHAI(j)/BETA(j) */
/*          may easily over- or underflow, and BETA(j) may even be zero. */
/*          Thus, the user should avoid naively computing the ratio */
/*          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). */

/*  VSL     (output) REAL 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) REAL 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) REAL 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(1,4*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 + 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.  (A,B) are not in Schur */
/*                form, 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 SGGBAK (computing VSL) */
/*                =N+8: error return from SGGBAK (computing VSR) */
/*                =N+9: error return from SLASCL (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;
    --alphar;
    --alphai;
    --beta;
    vsl_dim1 = *ldvsl;
    vsl_offset = 1 + vsl_dim1;
    vsl -= vsl_offset;
    vsr_dim1 = *ldvsr;
    vsr_offset = 1 + vsr_dim1;
    vsr -= vsr_offset;
    --work;

    /* 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 << 2;
    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 (*ldvsl < 1 || ilvsl && *ldvsl < *n) {
	*info = -12;
    } else if (*ldvsr < 1 || ilvsr && *ldvsr < *n) {
	*info = -14;
    } else if (*lwork < lwkmin && ! lquery) {
	*info = -16;
    }

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

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

/*     Quick return if possible */

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

/*     Get machine constants */

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

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

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

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

    if (ilbscl) {
	slascl_("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 */
/*     Workspace layout:  (2*N words -- "work..." not actually used) */
/*        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, (ftnlen)1);
    if (iinfo != 0) {
	*info = *n + 1;
	goto L10;
    }

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

    irows = ihi + 1 - ilo;
    icols = *n + 1 - ilo;
    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 L10;
    }

    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, (ftnlen)1, (ftnlen)1);
    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 L10;
    }

    if (ilvsl) {
	slaset_("Full", n, n, &c_b36, &c_b37, &vsl[vsl_offset], ldvsl, (
		ftnlen)4);
	i__1 = irows - 1;
	i__2 = irows - 1;
	slacpy_("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;
	sorgqr_(&irows, &irows, &irows, &vsl[ilo + ilo * vsl_dim1], ldvsl, &
		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 L10;
	}
    }

    if (ilvsr) {
	slaset_("Full", n, n, &c_b36, &c_b37, &vsr[vsr_offset], ldvsr, (
		ftnlen)4);
    }

/*     Reduce to generalized Hessenberg form */

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

    iwork = itau;
    i__1 = *lwork + 1 - iwork;
    shgeqz_("S", jobvsl, jobvsr, n, &ilo, &ihi, &a[a_offset], lda, &b[
	    b_offset], ldb, &alphar[1], &alphai[1], &beta[1], &vsl[vsl_offset]
	    , ldvsl, &vsr[vsr_offset], ldvsr, &work[iwork], &i__1, &iinfo, (
	    ftnlen)1, (ftnlen)1, (ftnlen)1);
    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 L10;
    }

/*     Apply permutation to VSL and VSR */

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

/*     Undo scaling */

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

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

    return 0;

/*     End of SGEGS */

} /* sgegs_ */

