/* ../../../dependencies/lapack/src/sggev.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"

/* Table of constant values */

static integer c__1 = 1;
static integer c__0 = 0;
static real c_b26 = 0.f;
static real c_b27 = 1.f;

/* Subroutine */ int sggev_(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, ftnlen jobvl_len, ftnlen jobvr_len)
{
    /* 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;

    /* Builtin functions */
    double sqrt(doublereal);

    /* Local variables */
    static integer jc, in, jr, ihi, ilo;
    static real eps;
    static logical ilv;
    static real anrm, bnrm;
    static integer ierr, itau;
    static real temp;
    static logical ilvl, ilvr;
    static integer iwrk;
    extern logical lsame_(char *, char *, ftnlen, ftnlen);
    static integer ileft, icols, irows;
    extern /* Subroutine */ int slabad_(real *, real *), 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);
    extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen), sgghrd_(
	    char *, char *, integer *, integer *, integer *, real *, integer *
	    , real *, integer *, real *, integer *, real *, integer *, 
	    integer *, ftnlen, ftnlen);
    static logical ldumma[1];
    static char chtemp[1];
    static real bignum;
    extern /* Subroutine */ int slascl_(char *, integer *, integer *, real *, 
	    real *, integer *, integer *, real *, integer *, integer *, 
	    ftnlen);
    extern integer ilaenv_(integer *, char *, char *, integer *, integer *, 
	    integer *, integer *, ftnlen, 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), stgevc_(
	    char *, char *, logical *, integer *, real *, integer *, real *, 
	    integer *, real *, integer *, real *, integer *, integer *, 
	    integer *, real *, integer *, ftnlen, ftnlen);
    static real anrmto, 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 integer minwrk, maxwrk;
    static real smlnum;
    extern /* Subroutine */ int sorgqr_(integer *, integer *, integer *, real 
	    *, integer *, real *, real *, integer *, integer *);
    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 */
/*  ======= */

/*  SGGEV 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. */

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

/*  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. */

/*  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 in the pair (A,B). */
/*          On exit, A has been overwritten. */

/*  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 in the pair (A,B). */
/*          On exit, B has been overwritten. */

/*  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.  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) REAL 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) REAL 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. */

/*  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(1,8*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. */

/*  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 SHGEQZ. */
/*                =N+2: error return from STGEVC. */

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

/*     .. 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", (ftnlen)1, (ftnlen)1)) {
	ijobvl = 1;
	ilvl = FALSE_;
    } else if (lsame_(jobvl, "V", (ftnlen)1, (ftnlen)1)) {
	ijobvl = 2;
	ilvl = TRUE_;
    } else {
	ijobvl = -1;
	ilvl = FALSE_;
    }

    if (lsame_(jobvr, "N", (ftnlen)1, (ftnlen)1)) {
	ijobvr = 1;
	ilvr = FALSE_;
    } else if (lsame_(jobvr, "V", (ftnlen)1, (ftnlen)1)) {
	ijobvr = 2;
	ilvr = TRUE_;
    } else {
	ijobvr = -1;
	ilvr = FALSE_;
    }
    ilv = ilvl || ilvr;

/*     Test the input arguments */

    *info = 0;
    lquery = *lwork == -1;
    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;
    }

/*     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.) */

    minwrk = 1;
    if (*info == 0 && (*lwork >= 1 || lquery)) {
	maxwrk = *n * 7 + *n * ilaenv_(&c__1, "SGEQRF", " ", n, &c__1, n, &
		c__0, (ftnlen)6, (ftnlen)1);
/* Computing MAX */
	i__1 = 1, i__2 = *n << 3;
	minwrk = max(i__1,i__2);
	work[1] = (real) maxwrk;
    }

    if (*lwork < minwrk && ! lquery) {
	*info = -16;
    }

    if (*info != 0) {
	i__1 = -(*info);
	xerbla_("SGGEV ", &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_("P", (ftnlen)1);
    smlnum = slamch_("S", (ftnlen)1);
    bignum = 1.f / smlnum;
    slabad_(&smlnum, &bignum);
    smlnum = sqrt(smlnum) / 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__0, &c__0, &anrm, &anrmto, n, n, &a[a_offset], lda, &
		ierr, (ftnlen)1);
    }

/*     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__0, &c__0, &bnrm, &bnrmto, n, n, &b[b_offset], ldb, &
		ierr, (ftnlen)1);
    }

/*     Permute the matrices A, B to isolate eigenvalues if possible */
/*     (Workspace: need 6*N) */

    ileft = 1;
    iright = *n + 1;
    iwrk = iright + *n;
    sggbal_("P", n, &a[a_offset], lda, &b[b_offset], ldb, &ilo, &ihi, &work[
	    ileft], &work[iright], &work[iwrk], &ierr, (ftnlen)1);

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

    irows = ihi + 1 - ilo;
    if (ilv) {
	icols = *n + 1 - ilo;
    } else {
	icols = irows;
    }
    itau = iwrk;
    iwrk = itau + irows;
    i__1 = *lwork + 1 - iwrk;
    sgeqrf_(&irows, &icols, &b[ilo + ilo * b_dim1], ldb, &work[itau], &work[
	    iwrk], &i__1, &ierr);

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

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

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

    if (ilvl) {
	slaset_("Full", n, n, &c_b26, &c_b27, &vl[vl_offset], ldvl, (ftnlen)4)
		;
	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, (ftnlen)1);
	i__1 = *lwork + 1 - iwrk;
	sorgqr_(&irows, &irows, &irows, &vl[ilo + ilo * vl_dim1], ldvl, &work[
		itau], &work[iwrk], &i__1, &ierr);
    }

/*     Initialize VR */

    if (ilvr) {
	slaset_("Full", n, n, &c_b26, &c_b27, &vr[vr_offset], ldvr, (ftnlen)4)
		;
    }

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

    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, &ierr, (
		ftnlen)1, (ftnlen)1);
    } 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, &ierr, (ftnlen)1, (ftnlen)1);
    }

/*     Perform QZ algorithm (Compute eigenvalues, and optionally, the */
/*     Schur forms and Schur vectors) */
/*     (Workspace: need N) */

    iwrk = itau;
    if (ilv) {
	*(unsigned char *)chtemp = 'S';
    } else {
	*(unsigned char *)chtemp = 'E';
    }
    i__1 = *lwork + 1 - iwrk;
    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[iwrk], &i__1, &ierr, (ftnlen)1, 
	    (ftnlen)1, (ftnlen)1);
    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 L110;
    }

/*     Compute Eigenvectors */
/*     (Workspace: need 6*N) */

    if (ilv) {
	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[
		iwrk], &ierr, (ftnlen)1, (ftnlen)1);
	if (ierr != 0) {
	    *info = *n + 2;
	    goto L110;
	}

/*        Undo balancing on VL and VR and normalization */
/*        (Workspace: none needed) */

	if (ilvl) {
	    sggbak_("P", "L", n, &ilo, &ihi, &work[ileft], &work[iright], n, &
		    vl[vl_offset], ldvl, &ierr, (ftnlen)1, (ftnlen)1);
	    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 < smlnum) {
		    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, &ierr, (ftnlen)1, (ftnlen)1);
	    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 < smlnum) {
		    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 if necessary */

    if (ilascl) {
	slascl_("G", &c__0, &c__0, &anrmto, &anrm, n, &c__1, &alphar[1], n, &
		ierr, (ftnlen)1);
	slascl_("G", &c__0, &c__0, &anrmto, &anrm, n, &c__1, &alphai[1], n, &
		ierr, (ftnlen)1);
    }

    if (ilbscl) {
	slascl_("G", &c__0, &c__0, &bnrmto, &bnrm, n, &c__1, &beta[1], n, &
		ierr, (ftnlen)1);
    }

L110:

    work[1] = (real) maxwrk;

    return 0;

/*     End of SGGEV */

} /* sggev_ */