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

/* Subroutine */ int zgges_(char *jobvsl, char *jobvsr, char *sort, L_fp 
	selctg, integer *n, doublecomplex *a, integer *lda, doublecomplex *b, 
	integer *ldb, integer *sdim, doublecomplex *alpha, doublecomplex *
	beta, doublecomplex *vsl, integer *ldvsl, doublecomplex *vsr, integer 
	*ldvsr, doublecomplex *work, integer *lwork, doublereal *rwork, 
	logical *bwork, integer *info)
{
/*  -- LAPACK driver routine (version 3.1) --   
       Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..   
       November 2006   


    Purpose   
    =======   

    ZGGES computes for a pair of N-by-N complex nonsymmetric matrices   
    (A,B), the generalized eigenvalues, the generalized complex Schur   
    form (S, T), and optionally left and/or right Schur vectors (VSL   
    and VSR). This gives the generalized Schur factorization   

            (A,B) = ( (VSL)*S*(VSR)**H, (VSL)*T*(VSR)**H )   

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

    Optionally, it also orders the eigenvalues so that a selected cluster   
    of eigenvalues appears in the leading diagonal blocks of the upper   
    triangular matrix S and the upper triangular matrix T. The leading   
    columns of VSL and VSR then form an unitary basis for the   
    corresponding left and right eigenspaces (deflating subspaces).   

    (If only the generalized eigenvalues are needed, use the driver   
    ZGGEV instead, which is faster.)   

    A generalized eigenvalue for a pair of matrices (A,B) is 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 pair of matrices (S,T) is in generalized complex Schur form if S   
    and T are upper triangular and, in addition, the diagonal elements   
    of T are non-negative real numbers.   

    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.   

    SORT    (input) CHARACTER*1   
            Specifies whether or not to order the eigenvalues on the   
            diagonal of the generalized Schur form.   
            = 'N':  Eigenvalues are not ordered;   
            = 'S':  Eigenvalues are ordered (see SELCTG).   

    SELCTG  (external procedure) LOGICAL FUNCTION of two COMPLEX*16 arguments   
            SELCTG must be declared EXTERNAL in the calling subroutine.   
            If SORT = 'N', SELCTG is not referenced.   
            If SORT = 'S', SELCTG is used to select eigenvalues to sort   
            to the top left of the Schur form.   
            An eigenvalue ALPHA(j)/BETA(j) is selected if   
            SELCTG(ALPHA(j),BETA(j)) is true.   

            Note that a selected complex eigenvalue may no longer satisfy   
            SELCTG(ALPHA(j),BETA(j)) = .TRUE. after ordering, since   
            ordering may change the value of complex eigenvalues   
            (especially if the eigenvalue is ill-conditioned), in this   
            case INFO is set to N+2 (See INFO below).   

    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.   
            On exit, A has been overwritten by its generalized Schur   
            form S.   

    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.   
            On exit, B has been overwritten by its generalized Schur   
            form T.   

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

    SDIM    (output) INTEGER   
            If SORT = 'N', SDIM = 0.   
            If SORT = 'S', SDIM = number of eigenvalues (after sorting)   
            for which SELCTG is true.   

    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 ZGGES. 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.   
            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.   
            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 (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).   
            For good performance, LWORK must generally be larger.   

            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 (8*N)   

    BWORK   (workspace) LOGICAL array, dimension (N)   
            Not referenced if SORT = '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:  =N+1: other than QZ iteration failed in ZHGEQZ   
                  =N+2: after reordering, roundoff changed values of   
                        some complex eigenvalues so that leading   
                        eigenvalues in the Generalized Schur form no   
                        longer satisfy SELCTG=.TRUE.  This could also   
                        be caused due to scaling.   
                  =N+3: reordering falied in ZTGSEN.   

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


       Decode the input arguments   

       Parameter adjustments */
    /* Table of constant values */
    static doublecomplex c_b1 = {0.,0.};
    static doublecomplex c_b2 = {1.,0.};
    static integer c__1 = 1;
    static integer c__0 = 0;
    static integer c_n1 = -1;
    
    /* System generated locals */
    integer a_dim1, a_offset, b_dim1, b_offset, vsl_dim1, vsl_offset, 
	    vsr_dim1, vsr_offset, i__1, i__2;
    /* Builtin functions */
    double sqrt(doublereal);
    /* Local variables */
    static integer i__;
    static doublereal dif[2];
    static integer ihi, ilo;
    static doublereal eps, anrm, bnrm;
    static integer idum[1], ierr, itau, iwrk;
    static doublereal pvsl, pvsr;
    extern logical lsame_(char *, char *);
    static integer ileft, icols;
    static logical cursl, ilvsl, ilvsr;
    static integer irwrk, irows;
    extern /* Subroutine */ int dlabad_(doublereal *, doublereal *);
    extern doublereal dlamch_(char *);
    extern /* Subroutine */ int zggbak_(char *, char *, integer *, integer *, 
	    integer *, doublereal *, doublereal *, integer *, doublecomplex *,
	     integer *, integer *), zggbal_(char *, integer *,
	     doublecomplex *, integer *, doublecomplex *, integer *, integer *
	    , integer *, doublereal *, doublereal *, doublereal *, integer *);
    static logical ilascl, ilbscl;
    extern /* Subroutine */ int xerbla_(char *, integer *);
    extern integer ilaenv_(integer *, char *, char *, integer *, integer *, 
	    integer *, integer *, ftnlen, ftnlen);
    extern doublereal zlange_(char *, integer *, integer *, doublecomplex *, 
	    integer *, doublereal *);
    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 * 	    ), zlascl_(char *, integer *, integer *, 
	    doublereal *, doublereal *, integer *, integer *, doublecomplex *,
	     integer *, integer *);
    static integer ijobvr;
    extern /* Subroutine */ int zgeqrf_(integer *, integer *, doublecomplex *,
	     integer *, doublecomplex *, doublecomplex *, integer *, integer * );
    static doublereal anrmto;
    static integer lwkmin;
    static logical lastsl;
    static doublereal bnrmto;
    extern /* Subroutine */ int zlacpy_(char *, integer *, integer *, 
	    doublecomplex *, integer *, doublecomplex *, integer *), 
	    zlaset_(char *, integer *, integer *, doublecomplex *, 
	    doublecomplex *, doublecomplex *, integer *), zhgeqz_(
	    char *, char *, char *, integer *, integer *, integer *, 
	    doublecomplex *, integer *, doublecomplex *, integer *, 
	    doublecomplex *, doublecomplex *, doublecomplex *, integer *, 
	    doublecomplex *, integer *, doublecomplex *, integer *, 
	    doublereal *, integer *), ztgsen_(integer 
	    *, logical *, logical *, logical *, integer *, doublecomplex *, 
	    integer *, doublecomplex *, integer *, doublecomplex *, 
	    doublecomplex *, doublecomplex *, integer *, doublecomplex *, 
	    integer *, integer *, doublereal *, doublereal *, doublereal *, 
	    doublecomplex *, integer *, integer *, integer *, integer *);
    static doublereal smlnum;
    static logical wantst, lquery;
    static integer lwkopt;
    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 *);


    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;
    --bwork;

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

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

    wantst = lsame_(sort, "S");

/*     Test the input arguments */

    *info = 0;
    lquery = *lwork == -1;
    if (ijobvl <= 0) {
	*info = -1;
    } else if (ijobvr <= 0) {
	*info = -2;
    } else if (! wantst && ! lsame_(sort, "N")) {
	*info = -3;
    } else if (*n < 0) {
	*info = -5;
    } else if (*lda < max(1,*n)) {
	*info = -7;
    } else if (*ldb < max(1,*n)) {
	*info = -9;
    } else if (*ldvsl < 1 || ilvsl && *ldvsl < *n) {
	*info = -14;
    } else if (*ldvsr < 1 || ilvsr && *ldvsr < *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.) */

    if (*info == 0) {
/* Computing MAX */
	i__1 = 1, i__2 = *n << 1;
	lwkmin = max(i__1,i__2);
/* Computing MAX */
	i__1 = 1, i__2 = *n + *n * ilaenv_(&c__1, "ZGEQRF", " ", n, &c__1, n, 
		&c__0, (ftnlen)6, (ftnlen)1);
	lwkopt = max(i__1,i__2);
/* Computing MAX */
	i__1 = lwkopt, i__2 = *n + *n * ilaenv_(&c__1, "ZUNMQR", " ", n, &
		c__1, n, &c_n1, (ftnlen)6, (ftnlen)1);
	lwkopt = max(i__1,i__2);
	if (ilvsl) {
/* Computing MAX */
	    i__1 = lwkopt, i__2 = *n + *n * ilaenv_(&c__1, "ZUNGQR", " ", n, &
		    c__1, n, &c_n1, (ftnlen)6, (ftnlen)1);
	    lwkopt = max(i__1,i__2);
	}
	work[1].r = (doublereal) lwkopt, work[1].i = 0.;

	if (*lwork < lwkmin && ! lquery) {
	    *info = -18;
	}
    }

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

/*     Quick return if possible */

    if (*n == 0) {
	*sdim = 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 = zlange_("M", n, n, &a[a_offset], lda, &rwork[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__0, &c__0, &anrm, &anrmto, n, n, &a[a_offset], lda, &
		ierr);
    }

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

    bnrm = zlange_("M", n, n, &b[b_offset], ldb, &rwork[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__0, &c__0, &bnrm, &bnrmto, n, n, &b[b_offset], ldb, &
		ierr);
    }

/*     Permute the matrix to make it more nearly triangular   
       (Real Workspace: need 6*N) */

    ileft = 1;
    iright = *n + 1;
    irwrk = iright + *n;
    zggbal_("P", n, &a[a_offset], lda, &b[b_offset], ldb, &ilo, &ihi, &rwork[
	    ileft], &rwork[iright], &rwork[irwrk], &ierr);

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

    irows = ihi + 1 - ilo;
    icols = *n + 1 - ilo;
    itau = 1;
    iwrk = itau + irows;
    i__1 = *lwork + 1 - iwrk;
    zgeqrf_(&irows, &icols, &b[ilo + ilo * b_dim1], ldb, &work[itau], &work[
	    iwrk], &i__1, &ierr);

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

    i__1 = *lwork + 1 - iwrk;
    zunmqr_("L", "C", &irows, &icols, &irows, &b[ilo + ilo * b_dim1], ldb, &
	    work[itau], &a[ilo + ilo * a_dim1], lda, &work[iwrk], &i__1, &
	    ierr);

/*     Initialize VSL   
       (Complex Workspace: need N, prefer N*NB) */

    if (ilvsl) {
	zlaset_("Full", n, n, &c_b1, &c_b2, &vsl[vsl_offset], ldvsl);
	if (irows > 1) {
	    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);
	}
	i__1 = *lwork + 1 - iwrk;
	zungqr_(&irows, &irows, &irows, &vsl[ilo + ilo * vsl_dim1], ldvsl, &
		work[itau], &work[iwrk], &i__1, &ierr);
    }

/*     Initialize VSR */

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

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

    zgghrd_(jobvsl, jobvsr, n, &ilo, &ihi, &a[a_offset], lda, &b[b_offset], 
	    ldb, &vsl[vsl_offset], ldvsl, &vsr[vsr_offset], ldvsr, &ierr);

    *sdim = 0;

/*     Perform QZ algorithm, computing Schur vectors if desired   
       (Complex Workspace: need N)   
       (Real Workspace: need N) */

    iwrk = itau;
    i__1 = *lwork + 1 - iwrk;
    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[iwrk], &i__1, &rwork[irwrk], &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 L30;
    }

/*     Sort eigenvalues ALPHA/BETA if desired   
       (Workspace: none needed) */

    if (wantst) {

/*        Undo scaling on eigenvalues before selecting */

	if (ilascl) {
	    zlascl_("G", &c__0, &c__0, &anrm, &anrmto, n, &c__1, &alpha[1], n,
		     &ierr);
	}
	if (ilbscl) {
	    zlascl_("G", &c__0, &c__0, &bnrm, &bnrmto, n, &c__1, &beta[1], n, 
		    &ierr);
	}

/*        Select eigenvalues */

	i__1 = *n;
	for (i__ = 1; i__ <= i__1; ++i__) {
	    bwork[i__] = (*selctg)(&alpha[i__], &beta[i__]);
/* L10: */
	}

	i__1 = *lwork - iwrk + 1;
	ztgsen_(&c__0, &ilvsl, &ilvsr, &bwork[1], n, &a[a_offset], lda, &b[
		b_offset], ldb, &alpha[1], &beta[1], &vsl[vsl_offset], ldvsl, 
		&vsr[vsr_offset], ldvsr, sdim, &pvsl, &pvsr, dif, &work[iwrk],
		 &i__1, idum, &c__1, &ierr);
	if (ierr == 1) {
	    *info = *n + 3;
	}

    }

/*     Apply back-permutation to VSL and VSR   
       (Workspace: none needed) */

    if (ilvsl) {
	zggbak_("P", "L", n, &ilo, &ihi, &rwork[ileft], &rwork[iright], n, &
		vsl[vsl_offset], ldvsl, &ierr);
    }
    if (ilvsr) {
	zggbak_("P", "R", n, &ilo, &ihi, &rwork[ileft], &rwork[iright], n, &
		vsr[vsr_offset], ldvsr, &ierr);
    }

/*     Undo scaling */

    if (ilascl) {
	zlascl_("U", &c__0, &c__0, &anrmto, &anrm, n, n, &a[a_offset], lda, &
		ierr);
	zlascl_("G", &c__0, &c__0, &anrmto, &anrm, n, &c__1, &alpha[1], n, &
		ierr);
    }

    if (ilbscl) {
	zlascl_("U", &c__0, &c__0, &bnrmto, &bnrm, n, n, &b[b_offset], ldb, &
		ierr);
	zlascl_("G", &c__0, &c__0, &bnrmto, &bnrm, n, &c__1, &beta[1], n, &
		ierr);
    }

    if (wantst) {

/*        Check if reordering is correct */

	lastsl = TRUE_;
	*sdim = 0;
	i__1 = *n;
	for (i__ = 1; i__ <= i__1; ++i__) {
	    cursl = (*selctg)(&alpha[i__], &beta[i__]);
	    if (cursl) {
		++(*sdim);
	    }
	    if (cursl && ! lastsl) {
		*info = *n + 2;
	    }
	    lastsl = cursl;
/* L20: */
	}

    }

L30:

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

    return 0;

/*     End of ZGGES */

} /* zgges_ */