starpu-max/min-dgels/base/SRC/dtgsna.c

/* dtgsna.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 doublereal c_b19 = 1.;
static doublereal c_b21 = 0.;
static integer c__2 = 2;
static logical c_false = FALSE_;
static integer c__3 = 3;

/* Subroutine */ int dtgsna_(char *job, char *howmny, logical *select, 
	integer *n, doublereal *a, integer *lda, doublereal *b, integer *ldb, 
	doublereal *vl, integer *ldvl, doublereal *vr, integer *ldvr, 
	doublereal *s, doublereal *dif, integer *mm, integer *m, doublereal *
	work, integer *lwork, integer *iwork, integer *info)
{
    /* System generated locals */
    integer a_dim1, a_offset, b_dim1, b_offset, vl_dim1, vl_offset, vr_dim1, 
	    vr_offset, i__1, i__2;
    doublereal d__1, d__2;

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

    /* Local variables */
    integer i__, k;
    doublereal c1, c2;
    integer n1, n2, ks, iz;
    doublereal eps, beta, cond;
    extern doublereal ddot_(integer *, doublereal *, integer *, doublereal *, 
	    integer *);
    logical pair;
    integer ierr;
    doublereal uhav, uhbv;
    integer ifst;
    doublereal lnrm;
    integer ilst;
    doublereal rnrm;
    extern /* Subroutine */ int dlag2_(doublereal *, integer *, doublereal *, 
	    integer *, doublereal *, doublereal *, doublereal *, doublereal *, 
	     doublereal *, doublereal *);
    extern doublereal dnrm2_(integer *, doublereal *, integer *);
    doublereal root1, root2, scale;
    extern logical lsame_(char *, char *);
    extern /* Subroutine */ int dgemv_(char *, integer *, integer *, 
	    doublereal *, doublereal *, integer *, doublereal *, integer *, 
	    doublereal *, doublereal *, integer *);
    doublereal uhavi, uhbvi, tmpii;
    integer lwmin;
    logical wants;
    doublereal tmpir, tmpri, dummy[1], tmprr;
    extern doublereal dlapy2_(doublereal *, doublereal *);
    doublereal dummy1[1];
    extern doublereal dlamch_(char *);
    doublereal alphai, alphar;
    extern /* Subroutine */ int dlacpy_(char *, integer *, integer *, 
	    doublereal *, integer *, doublereal *, integer *), 
	    xerbla_(char *, integer *), dtgexc_(logical *, logical *, 
	    integer *, doublereal *, integer *, doublereal *, integer *, 
	    doublereal *, integer *, doublereal *, integer *, integer *, 
	    integer *, doublereal *, integer *, integer *);
    logical wantbh, wantdf, somcon;
    doublereal alprqt;
    extern /* Subroutine */ int dtgsyl_(char *, integer *, integer *, integer 
	    *, doublereal *, integer *, doublereal *, integer *, doublereal *, 
	     integer *, doublereal *, integer *, doublereal *, integer *, 
	    doublereal *, integer *, doublereal *, doublereal *, doublereal *, 
	     integer *, integer *, integer *);
    doublereal smlnum;
    logical lquery;


/*  -- LAPACK routine (version 3.2) -- */
/*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/*     November 2006 */

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

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

/*  DTGSNA estimates reciprocal condition numbers for specified */
/*  eigenvalues and/or eigenvectors of a matrix pair (A, B) in */
/*  generalized real Schur canonical form (or of any matrix pair */
/*  (Q*A*Z', Q*B*Z') with orthogonal matrices Q and Z, where */
/*  Z' denotes the transpose of Z. */

/*  (A, B) must be in generalized real Schur form (as returned by DGGES), */
/*  i.e. A is block upper triangular with 1-by-1 and 2-by-2 diagonal */
/*  blocks. B is upper triangular. */


/*  Arguments */
/*  ========= */

/*  JOB     (input) CHARACTER*1 */
/*          Specifies whether condition numbers are required for */
/*          eigenvalues (S) or eigenvectors (DIF): */
/*          = 'E': for eigenvalues only (S); */
/*          = 'V': for eigenvectors only (DIF); */
/*          = 'B': for both eigenvalues and eigenvectors (S and DIF). */

/*  HOWMNY  (input) CHARACTER*1 */
/*          = 'A': compute condition numbers for all eigenpairs; */
/*          = 'S': compute condition numbers for selected eigenpairs */
/*                 specified by the array SELECT. */

/*  SELECT  (input) LOGICAL array, dimension (N) */
/*          If HOWMNY = 'S', SELECT specifies the eigenpairs for which */
/*          condition numbers are required. To select condition numbers */
/*          for the eigenpair corresponding to a real eigenvalue w(j), */
/*          SELECT(j) must be set to .TRUE.. To select condition numbers */
/*          corresponding to a complex conjugate pair of eigenvalues w(j) */
/*          and w(j+1), either SELECT(j) or SELECT(j+1) or both, must be */
/*          set to .TRUE.. */
/*          If HOWMNY = 'A', SELECT is not referenced. */

/*  N       (input) INTEGER */
/*          The order of the square matrix pair (A, B). N >= 0. */

/*  A       (input) DOUBLE PRECISION array, dimension (LDA,N) */
/*          The upper quasi-triangular matrix A in the pair (A,B). */

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

/*  B       (input) DOUBLE PRECISION array, dimension (LDB,N) */
/*          The upper triangular matrix B in the pair (A,B). */

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

/*  VL      (input) DOUBLE PRECISION array, dimension (LDVL,M) */
/*          If JOB = 'E' or 'B', VL must contain left eigenvectors of */
/*          (A, B), corresponding to the eigenpairs specified by HOWMNY */
/*          and SELECT. The eigenvectors must be stored in consecutive */
/*          columns of VL, as returned by DTGEVC. */
/*          If JOB = 'V', VL is not referenced. */

/*  LDVL    (input) INTEGER */
/*          The leading dimension of the array VL. LDVL >= 1. */
/*          If JOB = 'E' or 'B', LDVL >= N. */

/*  VR      (input) DOUBLE PRECISION array, dimension (LDVR,M) */
/*          If JOB = 'E' or 'B', VR must contain right eigenvectors of */
/*          (A, B), corresponding to the eigenpairs specified by HOWMNY */
/*          and SELECT. The eigenvectors must be stored in consecutive */
/*          columns ov VR, as returned by DTGEVC. */
/*          If JOB = 'V', VR is not referenced. */

/*  LDVR    (input) INTEGER */
/*          The leading dimension of the array VR. LDVR >= 1. */
/*          If JOB = 'E' or 'B', LDVR >= N. */

/*  S       (output) DOUBLE PRECISION array, dimension (MM) */
/*          If JOB = 'E' or 'B', the reciprocal condition numbers of the */
/*          selected eigenvalues, stored in consecutive elements of the */
/*          array. For a complex conjugate pair of eigenvalues two */
/*          consecutive elements of S are set to the same value. Thus */
/*          S(j), DIF(j), and the j-th columns of VL and VR all */
/*          correspond to the same eigenpair (but not in general the */
/*          j-th eigenpair, unless all eigenpairs are selected). */
/*          If JOB = 'V', S is not referenced. */

/*  DIF     (output) DOUBLE PRECISION array, dimension (MM) */
/*          If JOB = 'V' or 'B', the estimated reciprocal condition */
/*          numbers of the selected eigenvectors, stored in consecutive */
/*          elements of the array. For a complex eigenvector two */
/*          consecutive elements of DIF are set to the same value. If */
/*          the eigenvalues cannot be reordered to compute DIF(j), DIF(j) */
/*          is set to 0; this can only occur when the true value would be */
/*          very small anyway. */
/*          If JOB = 'E', DIF is not referenced. */

/*  MM      (input) INTEGER */
/*          The number of elements in the arrays S and DIF. MM >= M. */

/*  M       (output) INTEGER */
/*          The number of elements of the arrays S and DIF used to store */
/*          the specified condition numbers; for each selected real */
/*          eigenvalue one element is used, and for each selected complex */
/*          conjugate pair of eigenvalues, two elements are used. */
/*          If HOWMNY = 'A', M is set to N. */

/*  WORK    (workspace/output) DOUBLE PRECISION 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,N). */
/*          If JOB = 'V' or 'B' LWORK >= 2*N*(N+2)+16. */

/*          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. */

/*  IWORK   (workspace) INTEGER array, dimension (N + 6) */
/*          If JOB = 'E', IWORK is not referenced. */

/*  INFO    (output) INTEGER */
/*          =0: Successful exit */
/*          <0: If INFO = -i, the i-th argument had an illegal value */


/*  Further Details */
/*  =============== */

/*  The reciprocal of the condition number of a generalized eigenvalue */
/*  w = (a, b) is defined as */

/*       S(w) = (|u'Av|**2 + |u'Bv|**2)**(1/2) / (norm(u)*norm(v)) */

/*  where u and v are the left and right eigenvectors of (A, B) */
/*  corresponding to w; |z| denotes the absolute value of the complex */
/*  number, and norm(u) denotes the 2-norm of the vector u. */
/*  The pair (a, b) corresponds to an eigenvalue w = a/b (= u'Av/u'Bv) */
/*  of the matrix pair (A, B). If both a and b equal zero, then (A B) is */
/*  singular and S(I) = -1 is returned. */

/*  An approximate error bound on the chordal distance between the i-th */
/*  computed generalized eigenvalue w and the corresponding exact */
/*  eigenvalue lambda is */

/*       chord(w, lambda) <= EPS * norm(A, B) / S(I) */

/*  where EPS is the machine precision. */

/*  The reciprocal of the condition number DIF(i) of right eigenvector u */
/*  and left eigenvector v corresponding to the generalized eigenvalue w */
/*  is defined as follows: */

/*  a) If the i-th eigenvalue w = (a,b) is real */

/*     Suppose U and V are orthogonal transformations such that */

/*                U'*(A, B)*V  = (S, T) = ( a   *  ) ( b  *  )  1 */
/*                                        ( 0  S22 ),( 0 T22 )  n-1 */
/*                                          1  n-1     1 n-1 */

/*     Then the reciprocal condition number DIF(i) is */

/*                Difl((a, b), (S22, T22)) = sigma-min( Zl ), */

/*     where sigma-min(Zl) denotes the smallest singular value of the */
/*     2(n-1)-by-2(n-1) matrix */

/*         Zl = [ kron(a, In-1)  -kron(1, S22) ] */
/*              [ kron(b, In-1)  -kron(1, T22) ] . */

/*     Here In-1 is the identity matrix of size n-1. kron(X, Y) is the */
/*     Kronecker product between the matrices X and Y. */

/*     Note that if the default method for computing DIF(i) is wanted */
/*     (see DLATDF), then the parameter DIFDRI (see below) should be */
/*     changed from 3 to 4 (routine DLATDF(IJOB = 2 will be used)). */
/*     See DTGSYL for more details. */

/*  b) If the i-th and (i+1)-th eigenvalues are complex conjugate pair, */

/*     Suppose U and V are orthogonal transformations such that */

/*                U'*(A, B)*V = (S, T) = ( S11  *   ) ( T11  *  )  2 */
/*                                       ( 0    S22 ),( 0    T22) n-2 */
/*                                         2    n-2     2    n-2 */

/*     and (S11, T11) corresponds to the complex conjugate eigenvalue */
/*     pair (w, conjg(w)). There exist unitary matrices U1 and V1 such */
/*     that */

/*         U1'*S11*V1 = ( s11 s12 )   and U1'*T11*V1 = ( t11 t12 ) */
/*                      (  0  s22 )                    (  0  t22 ) */

/*     where the generalized eigenvalues w = s11/t11 and */
/*     conjg(w) = s22/t22. */

/*     Then the reciprocal condition number DIF(i) is bounded by */

/*         min( d1, max( 1, |real(s11)/real(s22)| )*d2 ) */

/*     where, d1 = Difl((s11, t11), (s22, t22)) = sigma-min(Z1), where */
/*     Z1 is the complex 2-by-2 matrix */

/*              Z1 =  [ s11  -s22 ] */
/*                    [ t11  -t22 ], */

/*     This is done by computing (using real arithmetic) the */
/*     roots of the characteristical polynomial det(Z1' * Z1 - lambda I), */
/*     where Z1' denotes the conjugate transpose of Z1 and det(X) denotes */
/*     the determinant of X. */

/*     and d2 is an upper bound on Difl((S11, T11), (S22, T22)), i.e. an */
/*     upper bound on sigma-min(Z2), where Z2 is (2n-2)-by-(2n-2) */

/*              Z2 = [ kron(S11', In-2)  -kron(I2, S22) ] */
/*                   [ kron(T11', In-2)  -kron(I2, T22) ] */

/*     Note that if the default method for computing DIF is wanted (see */
/*     DLATDF), then the parameter DIFDRI (see below) should be changed */
/*     from 3 to 4 (routine DLATDF(IJOB = 2 will be used)). See DTGSYL */
/*     for more details. */

/*  For each eigenvalue/vector specified by SELECT, DIF stores a */
/*  Frobenius norm-based estimate of Difl. */

/*  An approximate error bound for the i-th computed eigenvector VL(i) or */
/*  VR(i) is given by */

/*             EPS * norm(A, B) / DIF(i). */

/*  See ref. [2-3] for more details and further references. */

/*  Based on contributions by */
/*     Bo Kagstrom and Peter Poromaa, Department of Computing Science, */
/*     Umea University, S-901 87 Umea, Sweden. */

/*  References */
/*  ========== */

/*  [1] B. Kagstrom; A Direct Method for Reordering Eigenvalues in the */
/*      Generalized Real Schur Form of a Regular Matrix Pair (A, B), in */
/*      M.S. Moonen et al (eds), Linear Algebra for Large Scale and */
/*      Real-Time Applications, Kluwer Academic Publ. 1993, pp 195-218. */

/*  [2] B. Kagstrom and P. Poromaa; Computing Eigenspaces with Specified */
/*      Eigenvalues of a Regular Matrix Pair (A, B) and Condition */
/*      Estimation: Theory, Algorithms and Software, */
/*      Report UMINF - 94.04, Department of Computing Science, Umea */
/*      University, S-901 87 Umea, Sweden, 1994. Also as LAPACK Working */
/*      Note 87. To appear in Numerical Algorithms, 1996. */

/*  [3] B. Kagstrom and P. Poromaa, LAPACK-Style Algorithms and Software */
/*      for Solving the Generalized Sylvester Equation and Estimating the */
/*      Separation between Regular Matrix Pairs, Report UMINF - 93.23, */
/*      Department of Computing Science, Umea University, S-901 87 Umea, */
/*      Sweden, December 1993, Revised April 1994, Also as LAPACK Working */
/*      Note 75.  To appear in ACM Trans. on Math. Software, Vol 22, */
/*      No 1, 1996. */

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

/*     .. Parameters .. */
/*     .. */
/*     .. Local Scalars .. */
/*     .. */
/*     .. Local Arrays .. */
/*     .. */
/*     .. External Functions .. */
/*     .. */
/*     .. External Subroutines .. */
/*     .. */
/*     .. Intrinsic Functions .. */
/*     .. */
/*     .. Executable Statements .. */

/*     Decode and test the input parameters */

    /* Parameter adjustments */
    --select;
    a_dim1 = *lda;
    a_offset = 1 + a_dim1;
    a -= a_offset;
    b_dim1 = *ldb;
    b_offset = 1 + b_dim1;
    b -= b_offset;
    vl_dim1 = *ldvl;
    vl_offset = 1 + vl_dim1;
    vl -= vl_offset;
    vr_dim1 = *ldvr;
    vr_offset = 1 + vr_dim1;
    vr -= vr_offset;
    --s;
    --dif;
    --work;
    --iwork;

    /* Function Body */
    wantbh = lsame_(job, "B");
    wants = lsame_(job, "E") || wantbh;
    wantdf = lsame_(job, "V") || wantbh;

    somcon = lsame_(howmny, "S");

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

    if (! wants && ! wantdf) {
	*info = -1;
    } else if (! lsame_(howmny, "A") && ! somcon) {
	*info = -2;
    } else if (*n < 0) {
	*info = -4;
    } else if (*lda < max(1,*n)) {
	*info = -6;
    } else if (*ldb < max(1,*n)) {
	*info = -8;
    } else if (wants && *ldvl < *n) {
	*info = -10;
    } else if (wants && *ldvr < *n) {
	*info = -12;
    } else {

/*        Set M to the number of eigenpairs for which condition numbers */
/*        are required, and test MM. */

	if (somcon) {
	    *m = 0;
	    pair = FALSE_;
	    i__1 = *n;
	    for (k = 1; k <= i__1; ++k) {
		if (pair) {
		    pair = FALSE_;
		} else {
		    if (k < *n) {
			if (a[k + 1 + k * a_dim1] == 0.) {
			    if (select[k]) {
				++(*m);
			    }
			} else {
			    pair = TRUE_;
			    if (select[k] || select[k + 1]) {
				*m += 2;
			    }
			}
		    } else {
			if (select[*n]) {
			    ++(*m);
			}
		    }
		}
/* L10: */
	    }
	} else {
	    *m = *n;
	}

	if (*n == 0) {
	    lwmin = 1;
	} else if (lsame_(job, "V") || lsame_(job, 
		"B")) {
	    lwmin = (*n << 1) * (*n + 2) + 16;
	} else {
	    lwmin = *n;
	}
	work[1] = (doublereal) lwmin;

	if (*mm < *m) {
	    *info = -15;
	} else if (*lwork < lwmin && ! lquery) {
	    *info = -18;
	}
    }

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

/*     Quick return if possible */

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

/*     Get machine constants */

    eps = dlamch_("P");
    smlnum = dlamch_("S") / eps;
    ks = 0;
    pair = FALSE_;

    i__1 = *n;
    for (k = 1; k <= i__1; ++k) {

/*        Determine whether A(k,k) begins a 1-by-1 or 2-by-2 block. */

	if (pair) {
	    pair = FALSE_;
	    goto L20;
	} else {
	    if (k < *n) {
		pair = a[k + 1 + k * a_dim1] != 0.;
	    }
	}

/*        Determine whether condition numbers are required for the k-th */
/*        eigenpair. */

	if (somcon) {
	    if (pair) {
		if (! select[k] && ! select[k + 1]) {
		    goto L20;
		}
	    } else {
		if (! select[k]) {
		    goto L20;
		}
	    }
	}

	++ks;

	if (wants) {

/*           Compute the reciprocal condition number of the k-th */
/*           eigenvalue. */

	    if (pair) {

/*              Complex eigenvalue pair. */

		d__1 = dnrm2_(n, &vr[ks * vr_dim1 + 1], &c__1);
		d__2 = dnrm2_(n, &vr[(ks + 1) * vr_dim1 + 1], &c__1);
		rnrm = dlapy2_(&d__1, &d__2);
		d__1 = dnrm2_(n, &vl[ks * vl_dim1 + 1], &c__1);
		d__2 = dnrm2_(n, &vl[(ks + 1) * vl_dim1 + 1], &c__1);
		lnrm = dlapy2_(&d__1, &d__2);
		dgemv_("N", n, n, &c_b19, &a[a_offset], lda, &vr[ks * vr_dim1 
			+ 1], &c__1, &c_b21, &work[1], &c__1);
		tmprr = ddot_(n, &work[1], &c__1, &vl[ks * vl_dim1 + 1], &
			c__1);
		tmpri = ddot_(n, &work[1], &c__1, &vl[(ks + 1) * vl_dim1 + 1], 
			 &c__1);
		dgemv_("N", n, n, &c_b19, &a[a_offset], lda, &vr[(ks + 1) * 
			vr_dim1 + 1], &c__1, &c_b21, &work[1], &c__1);
		tmpii = ddot_(n, &work[1], &c__1, &vl[(ks + 1) * vl_dim1 + 1], 
			 &c__1);
		tmpir = ddot_(n, &work[1], &c__1, &vl[ks * vl_dim1 + 1], &
			c__1);
		uhav = tmprr + tmpii;
		uhavi = tmpir - tmpri;
		dgemv_("N", n, n, &c_b19, &b[b_offset], ldb, &vr[ks * vr_dim1 
			+ 1], &c__1, &c_b21, &work[1], &c__1);
		tmprr = ddot_(n, &work[1], &c__1, &vl[ks * vl_dim1 + 1], &
			c__1);
		tmpri = ddot_(n, &work[1], &c__1, &vl[(ks + 1) * vl_dim1 + 1], 
			 &c__1);
		dgemv_("N", n, n, &c_b19, &b[b_offset], ldb, &vr[(ks + 1) * 
			vr_dim1 + 1], &c__1, &c_b21, &work[1], &c__1);
		tmpii = ddot_(n, &work[1], &c__1, &vl[(ks + 1) * vl_dim1 + 1], 
			 &c__1);
		tmpir = ddot_(n, &work[1], &c__1, &vl[ks * vl_dim1 + 1], &
			c__1);
		uhbv = tmprr + tmpii;
		uhbvi = tmpir - tmpri;
		uhav = dlapy2_(&uhav, &uhavi);
		uhbv = dlapy2_(&uhbv, &uhbvi);
		cond = dlapy2_(&uhav, &uhbv);
		s[ks] = cond / (rnrm * lnrm);
		s[ks + 1] = s[ks];

	    } else {

/*              Real eigenvalue. */

		rnrm = dnrm2_(n, &vr[ks * vr_dim1 + 1], &c__1);
		lnrm = dnrm2_(n, &vl[ks * vl_dim1 + 1], &c__1);
		dgemv_("N", n, n, &c_b19, &a[a_offset], lda, &vr[ks * vr_dim1 
			+ 1], &c__1, &c_b21, &work[1], &c__1);
		uhav = ddot_(n, &work[1], &c__1, &vl[ks * vl_dim1 + 1], &c__1)
			;
		dgemv_("N", n, n, &c_b19, &b[b_offset], ldb, &vr[ks * vr_dim1 
			+ 1], &c__1, &c_b21, &work[1], &c__1);
		uhbv = ddot_(n, &work[1], &c__1, &vl[ks * vl_dim1 + 1], &c__1)
			;
		cond = dlapy2_(&uhav, &uhbv);
		if (cond == 0.) {
		    s[ks] = -1.;
		} else {
		    s[ks] = cond / (rnrm * lnrm);
		}
	    }
	}

	if (wantdf) {
	    if (*n == 1) {
		dif[ks] = dlapy2_(&a[a_dim1 + 1], &b[b_dim1 + 1]);
		goto L20;
	    }

/*           Estimate the reciprocal condition number of the k-th */
/*           eigenvectors. */
	    if (pair) {

/*              Copy the  2-by 2 pencil beginning at (A(k,k), B(k, k)). */
/*              Compute the eigenvalue(s) at position K. */

		work[1] = a[k + k * a_dim1];
		work[2] = a[k + 1 + k * a_dim1];
		work[3] = a[k + (k + 1) * a_dim1];
		work[4] = a[k + 1 + (k + 1) * a_dim1];
		work[5] = b[k + k * b_dim1];
		work[6] = b[k + 1 + k * b_dim1];
		work[7] = b[k + (k + 1) * b_dim1];
		work[8] = b[k + 1 + (k + 1) * b_dim1];
		d__1 = smlnum * eps;
		dlag2_(&work[1], &c__2, &work[5], &c__2, &d__1, &beta, dummy1, 
			 &alphar, dummy, &alphai);
		alprqt = 1.;
		c1 = (alphar * alphar + alphai * alphai + beta * beta) * 2.;
		c2 = beta * 4. * beta * alphai * alphai;
		root1 = c1 + sqrt(c1 * c1 - c2 * 4.);
		root2 = c2 / root1;
		root1 /= 2.;
/* Computing MIN */
		d__1 = sqrt(root1), d__2 = sqrt(root2);
		cond = min(d__1,d__2);
	    }

/*           Copy the matrix (A, B) to the array WORK and swap the */
/*           diagonal block beginning at A(k,k) to the (1,1) position. */

	    dlacpy_("Full", n, n, &a[a_offset], lda, &work[1], n);
	    dlacpy_("Full", n, n, &b[b_offset], ldb, &work[*n * *n + 1], n);
	    ifst = k;
	    ilst = 1;

	    i__2 = *lwork - (*n << 1) * *n;
	    dtgexc_(&c_false, &c_false, n, &work[1], n, &work[*n * *n + 1], n, 
		     dummy, &c__1, dummy1, &c__1, &ifst, &ilst, &work[(*n * *
		    n << 1) + 1], &i__2, &ierr);

	    if (ierr > 0) {

/*              Ill-conditioned problem - swap rejected. */

		dif[ks] = 0.;
	    } else {

/*              Reordering successful, solve generalized Sylvester */
/*              equation for R and L, */
/*                         A22 * R - L * A11 = A12 */
/*                         B22 * R - L * B11 = B12, */
/*              and compute estimate of Difl((A11,B11), (A22, B22)). */

		n1 = 1;
		if (work[2] != 0.) {
		    n1 = 2;
		}
		n2 = *n - n1;
		if (n2 == 0) {
		    dif[ks] = cond;
		} else {
		    i__ = *n * *n + 1;
		    iz = (*n << 1) * *n + 1;
		    i__2 = *lwork - (*n << 1) * *n;
		    dtgsyl_("N", &c__3, &n2, &n1, &work[*n * n1 + n1 + 1], n, 
			    &work[1], n, &work[n1 + 1], n, &work[*n * n1 + n1 
			    + i__], n, &work[i__], n, &work[n1 + i__], n, &
			    scale, &dif[ks], &work[iz + 1], &i__2, &iwork[1], 
			    &ierr);

		    if (pair) {
/* Computing MIN */
			d__1 = max(1.,alprqt) * dif[ks];
			dif[ks] = min(d__1,cond);
		    }
		}
	    }
	    if (pair) {
		dif[ks + 1] = dif[ks];
	    }
	}
	if (pair) {
	    ++ks;
	}

L20:
	;
    }
    work[1] = (doublereal) lwmin;
    return 0;

/*     End of DTGSNA */

} /* dtgsna_ */