[] add metering mode to CLI

1 files changed, 811 insertions, 0 deletions

diff --git a/contrib/libs/clapack/sggesx.c b/contrib/libs/clapack/sggesx.c
new file mode 100644
index 0000000000..9128e03431
--- /dev/null
+++ b/contrib/libs/clapack/sggesx.c
@@ -0,0 +1,811 @@
+/* sggesx.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__0 = 0;
+static integer c_n1 = -1;
+static real c_b42 = 0.f;
+static real c_b43 = 1.f;
+
+/* Subroutine */ int sggesx_(char *jobvsl, char *jobvsr, char *sort, L_fp 
+	selctg, char *sense, integer *n, real *a, integer *lda, real *b, 
+	integer *ldb, integer *sdim, real *alphar, real *alphai, real *beta, 
+	real *vsl, integer *ldvsl, real *vsr, integer *ldvsr, real *rconde, 
+	real *rcondv, real *work, integer *lwork, integer *iwork, integer *
+	liwork, logical *bwork, integer *info)
+{
+    /* System generated locals */
+    integer a_dim1, a_offset, b_dim1, b_offset, vsl_dim1, vsl_offset, 
+	    vsr_dim1, vsr_offset, i__1, i__2;
+    real r__1;
+
+    /* Builtin functions */
+    double sqrt(doublereal);
+
+    /* Local variables */
+    integer i__, ip;
+    real pl, pr, dif[2];
+    integer ihi, ilo;
+    real eps;
+    integer ijob;
+    real anrm, bnrm;
+    integer ierr, itau, iwrk, lwrk;
+    extern logical lsame_(char *, char *);
+    integer ileft, icols;
+    logical cursl, ilvsl, ilvsr;
+    integer irows;
+    logical lst2sl;
+    extern /* Subroutine */ int slabad_(real *, real *), 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 *);
+    logical ilascl, ilbscl;
+    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;
+    extern /* Subroutine */ int xerbla_(char *, integer *);
+    real bignum;
+    extern /* Subroutine */ int slascl_(char *, integer *, integer *, real *, 
+	    real *, integer *, integer *, real *, integer *, integer *);
+    extern integer ilaenv_(integer *, char *, char *, integer *, integer *, 
+	    integer *, integer *);
+    integer ijobvl, iright;
+    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 *);
+    logical wantsb, wantse, lastsl;
+    integer liwmin;
+    real anrmto, bnrmto;
+    integer minwrk, maxwrk;
+    logical wantsn;
+    real smlnum;
+    extern /* Subroutine */ int shgeqz_(char *, char *, char *, integer *, 
+	    integer *, integer *, real *, integer *, real *, integer *, real *
+, real *, real *, real *, integer *, real *, integer *, real *, 
+	    integer *, integer *), slaset_(char *, 
+	    integer *, integer *, real *, real *, real *, integer *), 
+	    sorgqr_(integer *, integer *, integer *, real *, integer *, real *
+, real *, integer *, integer *), stgsen_(integer *, logical *, 
+	    logical *, logical *, integer *, real *, integer *, real *, 
+	    integer *, real *, real *, real *, real *, integer *, real *, 
+	    integer *, integer *, real *, real *, real *, real *, integer *, 
+	    integer *, integer *, integer *);
+    logical wantst, lquery, wantsv;
+    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 .. */
+/*     .. */
+/*     .. Function Arguments .. */
+/*     .. */
+
+/*  Purpose */
+/*  ======= */
+
+/*  SGGESX computes for a pair of N-by-N real nonsymmetric matrices */
+/*  (A,B), the generalized eigenvalues, the real Schur form (S,T), and, */
+/*  optionally, the left and/or right matrices of Schur vectors (VSL and */
+/*  VSR).  This gives the generalized Schur factorization */
+
+/*       (A,B) = ( (VSL) S (VSR)**T, (VSL) T (VSR)**T ) */
+
+/*  Optionally, it also orders the eigenvalues so that a selected cluster */
+/*  of eigenvalues appears in the leading diagonal blocks of the upper */
+/*  quasi-triangular matrix S and the upper triangular matrix T; computes */
+/*  a reciprocal condition number for the average of the selected */
+/*  eigenvalues (RCONDE); and computes a reciprocal condition number for */
+/*  the right and left deflating subspaces corresponding to the selected */
+/*  eigenvalues (RCONDV). The leading columns of VSL and VSR then form */
+/*  an orthonormal basis for the corresponding left and right eigenspaces */
+/*  (deflating subspaces). */
+
+/*  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 or for both being zero. */
+
+/*  A pair of matrices (S,T) is in generalized real Schur form if T is */
+/*  upper triangular with non-negative diagonal and S 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 S will be */
+/*  "standardized" by making the corresponding elements of T have the */
+/*  form: */
+/*          [  a  0  ] */
+/*          [  0  b  ] */
+
+/*  and the pair of corresponding 2-by-2 blocks in S and T will have a */
+/*  complex conjugate pair of generalized eigenvalues. */
+
+
+/*  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 three REAL 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 (ALPHAR(j)+ALPHAI(j))/BETA(j) is selected if */
+/*          SELCTG(ALPHAR(j),ALPHAI(j),BETA(j)) is true; i.e. if either */
+/*          one of a complex conjugate pair of eigenvalues is selected, */
+/*          then both complex eigenvalues are selected. */
+/*          Note that a selected complex eigenvalue may no longer satisfy */
+/*          SELCTG(ALPHAR(j),ALPHAI(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+3. */
+
+/*  SENSE   (input) CHARACTER*1 */
+/*          Determines which reciprocal condition numbers are computed. */
+/*          = 'N' : None are computed; */
+/*          = 'E' : Computed for average of selected eigenvalues only; */
+/*          = 'V' : Computed for selected deflating subspaces only; */
+/*          = 'B' : Computed for both. */
+/*          If SENSE = 'E', 'V', or 'B', SORT must equal 'S'. */
+
+/*  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. */
+/*          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) REAL 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.  (Complex conjugate pairs for which */
+/*          SELCTG is true for either eigenvalue count as 2.) */
+
+/*  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 */
+/*          and BETA(j),j=1,...,N  are the diagonals of the complex Schur */
+/*          form (S,T) 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. */
+/*          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. */
+/*          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. */
+/*          Not referenced if JOBVSR = 'N'. */
+
+/*  LDVSR   (input) INTEGER */
+/*          The leading dimension of the matrix VSR. LDVSR >= 1, and */
+/*          if JOBVSR = 'V', LDVSR >= N. */
+
+/*  RCONDE  (output) REAL array, dimension ( 2 ) */
+/*          If SENSE = 'E' or 'B', RCONDE(1) and RCONDE(2) contain the */
+/*          reciprocal condition numbers for the average of the selected */
+/*          eigenvalues. */
+/*          Not referenced if SENSE = 'N' or 'V'. */
+
+/*  RCONDV  (output) REAL array, dimension ( 2 ) */
+/*          If SENSE = 'V' or 'B', RCONDV(1) and RCONDV(2) contain the */
+/*          reciprocal condition numbers for the selected deflating */
+/*          subspaces. */
+/*          Not referenced if SENSE = 'N' or 'E'. */
+
+/*  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. */
+/*          If N = 0, LWORK >= 1, else if SENSE = 'E', 'V', or 'B', */
+/*          LWORK >= max( 8*N, 6*N+16, 2*SDIM*(N-SDIM) ), else */
+/*          LWORK >= max( 8*N, 6*N+16 ). */
+/*          Note that 2*SDIM*(N-SDIM) <= N*N/2. */
+/*          Note also that an error is only returned if */
+/*          LWORK < max( 8*N, 6*N+16), but if SENSE = 'E' or 'V' or 'B' */
+/*          this may not be large enough. */
+
+/*          If LWORK = -1, then a workspace query is assumed; the routine */
+/*          only calculates the bound on the optimal size of the WORK */
+/*          array and the minimum size of the IWORK array, returns these */
+/*          values as the first entries of the WORK and IWORK arrays, and */
+/*          no error message related to LWORK or LIWORK is issued by */
+/*          XERBLA. */
+
+/*  IWORK   (workspace) INTEGER array, dimension (MAX(1,LIWORK)) */
+/*          On exit, if INFO = 0, IWORK(1) returns the minimum LIWORK. */
+
+/*  LIWORK  (input) INTEGER */
+/*          The dimension of the array IWORK. */
+/*          If SENSE = 'N' or N = 0, LIWORK >= 1, otherwise */
+/*          LIWORK >= N+6. */
+
+/*          If LIWORK = -1, then a workspace query is assumed; the */
+/*          routine only calculates the bound on the optimal size of the */
+/*          WORK array and the minimum size of the IWORK array, returns */
+/*          these values as the first entries of the WORK and IWORK */
+/*          arrays, and no error message related to LWORK or LIWORK is */
+/*          issued by XERBLA. */
+
+/*  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 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: 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 failed in STGSEN. */
+
+/*  Further details */
+/*  =============== */
+
+/*  An approximate (asymptotic) bound on the average absolute error of */
+/*  the selected eigenvalues is */
+
+/*       EPS * norm((A, B)) / RCONDE( 1 ). */
+
+/*  An approximate (asymptotic) bound on the maximum angular error in */
+/*  the computed deflating subspaces is */
+
+/*       EPS * norm((A, B)) / RCONDV( 2 ). */
+
+/*  See LAPACK User's Guide, section 4.11 for more information. */
+
+/*  ===================================================================== */
+
+/*     .. 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;
+    vsl_dim1 = *ldvsl;
+    vsl_offset = 1 + vsl_dim1;
+    vsl -= vsl_offset;
+    vsr_dim1 = *ldvsr;
+    vsr_offset = 1 + vsr_dim1;
+    vsr -= vsr_offset;
+    --rconde;
+    --rcondv;
+    --work;
+    --iwork;
+    --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");
+    wantsn = lsame_(sense, "N");
+    wantse = lsame_(sense, "E");
+    wantsv = lsame_(sense, "V");
+    wantsb = lsame_(sense, "B");
+    lquery = *lwork == -1 || *liwork == -1;
+    if (wantsn) {
+	ijob = 0;
+    } else if (wantse) {
+	ijob = 1;
+    } else if (wantsv) {
+	ijob = 2;
+    } else if (wantsb) {
+	ijob = 4;
+    }
+
+/*     Test the input arguments */
+
+    *info = 0;
+    if (ijobvl <= 0) {
+	*info = -1;
+    } else if (ijobvr <= 0) {
+	*info = -2;
+    } else if (! wantst && ! lsame_(sort, "N")) {
+	*info = -3;
+    } else if (! (wantsn || wantse || wantsv || wantsb) || ! wantst && ! 
+	    wantsn) {
+	*info = -5;
+    } else if (*n < 0) {
+	*info = -6;
+    } else if (*lda < max(1,*n)) {
+	*info = -8;
+    } else if (*ldb < max(1,*n)) {
+	*info = -10;
+    } else if (*ldvsl < 1 || ilvsl && *ldvsl < *n) {
+	*info = -16;
+    } else if (*ldvsr < 1 || ilvsr && *ldvsr < *n) {
+	*info = -18;
+    }
+
+/*     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) {
+	if (*n > 0) {
+/* Computing MAX */
+	    i__1 = *n << 3, i__2 = *n * 6 + 16;
+	    minwrk = max(i__1,i__2);
+	    maxwrk = minwrk - *n + *n * ilaenv_(&c__1, "SGEQRF", " ", n, &
+		    c__1, n, &c__0);
+/* Computing MAX */
+	    i__1 = maxwrk, i__2 = minwrk - *n + *n * ilaenv_(&c__1, "SORMQR", 
+		    " ", n, &c__1, n, &c_n1);
+	    maxwrk = max(i__1,i__2);
+	    if (ilvsl) {
+/* Computing MAX */
+		i__1 = maxwrk, i__2 = minwrk - *n + *n * ilaenv_(&c__1, "SOR"
+			"GQR", " ", n, &c__1, n, &c_n1);
+		maxwrk = max(i__1,i__2);
+	    }
+	    lwrk = maxwrk;
+	    if (ijob >= 1) {
+/* Computing MAX */
+		i__1 = lwrk, i__2 = *n * *n / 2;
+		lwrk = max(i__1,i__2);
+	    }
+	} else {
+	    minwrk = 1;
+	    maxwrk = 1;
+	    lwrk = 1;
+	}
+	work[1] = (real) lwrk;
+	if (wantsn || *n == 0) {
+	    liwmin = 1;
+	} else {
+	    liwmin = *n + 6;
+	}
+	iwork[1] = liwmin;
+
+	if (*lwork < minwrk && ! lquery) {
+	    *info = -22;
+	} else if (*liwork < liwmin && ! lquery) {
+	    *info = -24;
+	}
+    }
+
+    if (*info != 0) {
+	i__1 = -(*info);
+	xerbla_("SGGESX", &i__1);
+	return 0;
+    } else if (lquery) {
+	return 0;
+    }
+
+/*     Quick return if possible */
+
+    if (*n == 0) {
+	*sdim = 0;
+	return 0;
+    }
+
+/*     Get machine constants */
+
+    eps = slamch_("P");
+    safmin = slamch_("S");
+    safmax = 1.f / safmin;
+    slabad_(&safmin, &safmax);
+    smlnum = sqrt(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]);
+    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);
+    }
+
+/*     Scale B if max element outside range [SMLNUM,BIGNUM] */
+
+    bnrm = slange_("M", n, n, &b[b_offset], ldb, &work[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);
+    }
+
+/*     Permute the matrix to make it more nearly triangular */
+/*     (Workspace: need 6*N + 2*N for permutation parameters) */
+
+    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);
+
+/*     Reduce B to triangular form (QR decomposition of B) */
+/*     (Workspace: need N, prefer N*NB) */
+
+    irows = ihi + 1 - ilo;
+    icols = *n + 1 - ilo;
+    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);
+
+/*     Initialize VSL */
+/*     (Workspace: need N, prefer N*NB) */
+
+    if (ilvsl) {
+	slaset_("Full", n, n, &c_b42, &c_b43, &vsl[vsl_offset], ldvsl);
+	if (irows > 1) {
+	    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);
+	}
+	i__1 = *lwork + 1 - iwrk;
+	sorgqr_(&irows, &irows, &irows, &vsl[ilo + ilo * vsl_dim1], ldvsl, &
+		work[itau], &work[iwrk], &i__1, &ierr);
+    }
+
+/*     Initialize VSR */
+
+    if (ilvsr) {
+	slaset_("Full", n, n, &c_b42, &c_b43, &vsr[vsr_offset], ldvsr);
+    }
+
+/*     Reduce to generalized Hessenberg form */
+/*     (Workspace: none needed) */
+
+    sgghrd_(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 */
+/*     (Workspace: need N) */
+
+    iwrk = itau;
+    i__1 = *lwork + 1 - iwrk;
+    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[iwrk], &i__1, &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 L50;
+    }
+
+/*     Sort eigenvalues ALPHA/BETA and compute the reciprocal of */
+/*     condition number(s) */
+/*     (Workspace: If IJOB >= 1, need MAX( 8*(N+1), 2*SDIM*(N-SDIM) ) */
+/*                 otherwise, need 8*(N+1) ) */
+
+    if (wantst) {
+
+/*        Undo scaling on eigenvalues before SELCTGing */
+
+	if (ilascl) {
+	    slascl_("G", &c__0, &c__0, &anrmto, &anrm, n, &c__1, &alphar[1], 
+		    n, &ierr);
+	    slascl_("G", &c__0, &c__0, &anrmto, &anrm, n, &c__1, &alphai[1], 
+		    n, &ierr);
+	}
+	if (ilbscl) {
+	    slascl_("G", &c__0, &c__0, &bnrmto, &bnrm, n, &c__1, &beta[1], n, 
+		    &ierr);
+	}
+
+/*        Select eigenvalues */
+
+	i__1 = *n;
+	for (i__ = 1; i__ <= i__1; ++i__) {
+	    bwork[i__] = (*selctg)(&alphar[i__], &alphai[i__], &beta[i__]);
+/* L10: */
+	}
+
+/*        Reorder eigenvalues, transform Generalized Schur vectors, and */
+/*        compute reciprocal condition numbers */
+
+	i__1 = *lwork - iwrk + 1;
+	stgsen_(&ijob, &ilvsl, &ilvsr, &bwork[1], n, &a[a_offset], lda, &b[
+		b_offset], ldb, &alphar[1], &alphai[1], &beta[1], &vsl[
+		vsl_offset], ldvsl, &vsr[vsr_offset], ldvsr, sdim, &pl, &pr, 
+		dif, &work[iwrk], &i__1, &iwork[1], liwork, &ierr);
+
+	if (ijob >= 1) {
+/* Computing MAX */
+	    i__1 = maxwrk, i__2 = (*sdim << 1) * (*n - *sdim);
+	    maxwrk = max(i__1,i__2);
+	}
+	if (ierr == -22) {
+
+/*            not enough real workspace */
+
+	    *info = -22;
+	} else {
+	    if (ijob == 1 || ijob == 4) {
+		rconde[1] = pl;
+		rconde[2] = pr;
+	    }
+	    if (ijob == 2 || ijob == 4) {
+		rcondv[1] = dif[0];
+		rcondv[2] = dif[1];
+	    }
+	    if (ierr == 1) {
+		*info = *n + 3;
+	    }
+	}
+
+    }
+
+/*     Apply permutation to VSL and VSR */
+/*     (Workspace: none needed) */
+
+    if (ilvsl) {
+	sggbak_("P", "L", n, &ilo, &ihi, &work[ileft], &work[iright], n, &vsl[
+		vsl_offset], ldvsl, &ierr);
+    }
+
+    if (ilvsr) {
+	sggbak_("P", "R", n, &ilo, &ihi, &work[ileft], &work[iright], n, &vsr[
+		vsr_offset], ldvsr, &ierr);
+    }
+
+/*     Check if unscaling would cause over/underflow, if so, rescale */
+/*     (ALPHAR(I),ALPHAI(I),BETA(I)) so BETA(I) is on the order of */
+/*     B(I,I) and ALPHAR(I) and ALPHAI(I) are on the order of A(I,I) */
+
+    if (ilascl) {
+	i__1 = *n;
+	for (i__ = 1; i__ <= i__1; ++i__) {
+	    if (alphai[i__] != 0.f) {
+		if (alphar[i__] / safmax > anrmto / anrm || safmin / alphar[
+			i__] > anrm / anrmto) {
+		    work[1] = (r__1 = a[i__ + i__ * a_dim1] / alphar[i__], 
+			    dabs(r__1));
+		    beta[i__] *= work[1];
+		    alphar[i__] *= work[1];
+		    alphai[i__] *= work[1];
+		} else if (alphai[i__] / safmax > anrmto / anrm || safmin / 
+			alphai[i__] > anrm / anrmto) {
+		    work[1] = (r__1 = a[i__ + (i__ + 1) * a_dim1] / alphai[
+			    i__], dabs(r__1));
+		    beta[i__] *= work[1];
+		    alphar[i__] *= work[1];
+		    alphai[i__] *= work[1];
+		}
+	    }
+/* L20: */
+	}
+    }
+
+    if (ilbscl) {
+	i__1 = *n;
+	for (i__ = 1; i__ <= i__1; ++i__) {
+	    if (alphai[i__] != 0.f) {
+		if (beta[i__] / safmax > bnrmto / bnrm || safmin / beta[i__] 
+			> bnrm / bnrmto) {
+		    work[1] = (r__1 = b[i__ + i__ * b_dim1] / beta[i__], dabs(
+			    r__1));
+		    beta[i__] *= work[1];
+		    alphar[i__] *= work[1];
+		    alphai[i__] *= work[1];
+		}
+	    }
+/* L25: */
+	}
+    }
+
+/*     Undo scaling */
+
+    if (ilascl) {
+	slascl_("H", &c__0, &c__0, &anrmto, &anrm, n, n, &a[a_offset], lda, &
+		ierr);
+	slascl_("G", &c__0, &c__0, &anrmto, &anrm, n, &c__1, &alphar[1], n, &
+		ierr);
+	slascl_("G", &c__0, &c__0, &anrmto, &anrm, n, &c__1, &alphai[1], n, &
+		ierr);
+    }
+
+    if (ilbscl) {
+	slascl_("U", &c__0, &c__0, &bnrmto, &bnrm, n, n, &b[b_offset], ldb, &
+		ierr);
+	slascl_("G", &c__0, &c__0, &bnrmto, &bnrm, n, &c__1, &beta[1], n, &
+		ierr);
+    }
+
+    if (wantst) {
+
+/*        Check if reordering is correct */
+
+	lastsl = TRUE_;
+	lst2sl = TRUE_;
+	*sdim = 0;
+	ip = 0;
+	i__1 = *n;
+	for (i__ = 1; i__ <= i__1; ++i__) {
+	    cursl = (*selctg)(&alphar[i__], &alphai[i__], &beta[i__]);
+	    if (alphai[i__] == 0.f) {
+		if (cursl) {
+		    ++(*sdim);
+		}
+		ip = 0;
+		if (cursl && ! lastsl) {
+		    *info = *n + 2;
+		}
+	    } else {
+		if (ip == 1) {
+
+/*                 Last eigenvalue of conjugate pair */
+
+		    cursl = cursl || lastsl;
+		    lastsl = cursl;
+		    if (cursl) {
+			*sdim += 2;
+		    }
+		    ip = -1;
+		    if (cursl && ! lst2sl) {
+			*info = *n + 2;
+		    }
+		} else {
+
+/*                 First eigenvalue of conjugate pair */
+
+		    ip = 1;
+		}
+	    }
+	    lst2sl = lastsl;
+	    lastsl = cursl;
+/* L40: */
+	}
+
+    }
+
+L50:
+
+    work[1] = (real) maxwrk;
+    iwork[1] = liwmin;
+
+    return 0;
+
+/*     End of SGGESX */
+
+} /* sggesx_ */