f2c/c/dtgsna.c

/* ../netlib/dtgsna.f -- translated by f2c (version 20100827). 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 "FLA_f2c.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;
/* > \brief \b DTGSNA */
/* =========== DOCUMENTATION =========== */
/* Online html documentation available at */
/* http://www.netlib.org/lapack/explore-html/ */
/* > \htmlonly */
/* > Download DTGSNA + dependencies */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dtgsna. f"> */
/* > [TGZ]</a> */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dtgsna. f"> */
/* > [ZIP]</a> */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dtgsna. f"> */
/* > [TXT]</a> */
/* > \endhtmlonly */
/* Definition: */
/* =========== */
/* SUBROUTINE DTGSNA( JOB, HOWMNY, SELECT, N, A, LDA, B, LDB, VL, */
/* LDVL, VR, LDVR, S, DIF, MM, M, WORK, LWORK, */
/* IWORK, INFO ) */
/* .. Scalar Arguments .. */
/* CHARACTER HOWMNY, JOB */
/* INTEGER INFO, LDA, LDB, LDVL, LDVR, LWORK, M, MM, N */
/* .. */
/* .. Array Arguments .. */
/* LOGICAL SELECT( * ) */
/* INTEGER IWORK( * ) */
/* DOUBLE PRECISION A( LDA, * ), B( LDB, * ), DIF( * ), S( * ), */
/* $ VL( LDVL, * ), VR( LDVR, * ), WORK( * ) */
/* .. */
/* > \par Purpose: */
/* ============= */
/* > */
/* > \verbatim */
/* > */
/* > 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**T, Q*B*Z**T) with orthogonal matrices Q and Z, where */
/* > Z**T 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. */
/* > */
/* > \endverbatim */
/* Arguments: */
/* ========== */
/* > \param[in] JOB */
/* > \verbatim */
/* > JOB is 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). */
/* > \endverbatim */
/* > */
/* > \param[in] HOWMNY */
/* > \verbatim */
/* > HOWMNY is CHARACTER*1 */
/* > = 'A': compute condition numbers for all eigenpairs;
*/
/* > = 'S': compute condition numbers for selected eigenpairs */
/* > specified by the array SELECT. */
/* > \endverbatim */
/* > */
/* > \param[in] SELECT */
/* > \verbatim */
/* > SELECT is 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. */
/* > \endverbatim */
/* > */
/* > \param[in] N */
/* > \verbatim */
/* > N is INTEGER */
/* > The order of the square matrix pair (A, B). N >= 0. */
/* > \endverbatim */
/* > */
/* > \param[in] A */
/* > \verbatim */
/* > A is DOUBLE PRECISION array, dimension (LDA,N) */
/* > The upper quasi-triangular matrix A in the pair (A,B). */
/* > \endverbatim */
/* > */
/* > \param[in] LDA */
/* > \verbatim */
/* > LDA is INTEGER */
/* > The leading dimension of the array A. LDA >= max(1,N). */
/* > \endverbatim */
/* > */
/* > \param[in] B */
/* > \verbatim */
/* > B is DOUBLE PRECISION array, dimension (LDB,N) */
/* > The upper triangular matrix B in the pair (A,B). */
/* > \endverbatim */
/* > */
/* > \param[in] LDB */
/* > \verbatim */
/* > LDB is INTEGER */
/* > The leading dimension of the array B. LDB >= max(1,N). */
/* > \endverbatim */
/* > */
/* > \param[in] VL */
/* > \verbatim */
/* > VL is 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. */
/* > \endverbatim */
/* > */
/* > \param[in] LDVL */
/* > \verbatim */
/* > LDVL is INTEGER */
/* > The leading dimension of the array VL. LDVL >= 1. */
/* > If JOB = 'E' or 'B', LDVL >= N. */
/* > \endverbatim */
/* > */
/* > \param[in] VR */
/* > \verbatim */
/* > VR is 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. */
/* > \endverbatim */
/* > */
/* > \param[in] LDVR */
/* > \verbatim */
/* > LDVR is INTEGER */
/* > The leading dimension of the array VR. LDVR >= 1. */
/* > If JOB = 'E' or 'B', LDVR >= N. */
/* > \endverbatim */
/* > */
/* > \param[out] S */
/* > \verbatim */
/* > S is 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. */
/* > \endverbatim */
/* > */
/* > \param[out] DIF */
/* > \verbatim */
/* > DIF is 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. */
/* > \endverbatim */
/* > */
/* > \param[in] MM */
/* > \verbatim */
/* > MM is INTEGER */
/* > The number of elements in the arrays S and DIF. MM >= M. */
/* > \endverbatim */
/* > */
/* > \param[out] M */
/* > \verbatim */
/* > M is 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. */
/* > \endverbatim */
/* > */
/* > \param[out] WORK */
/* > \verbatim */
/* > WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)) */
/* > On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */
/* > \endverbatim */
/* > */
/* > \param[in] LWORK */
/* > \verbatim */
/* > LWORK is 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. */
/* > \endverbatim */
/* > */
/* > \param[out] IWORK */
/* > \verbatim */
/* > IWORK is INTEGER array, dimension (N + 6) */
/* > If JOB = 'E', IWORK is not referenced. */
/* > \endverbatim */
/* > */
/* > \param[out] INFO */
/* > \verbatim */
/* > INFO is INTEGER */
/* > =0: Successful exit */
/* > <0: If INFO = -i, the i-th argument had an illegal value */
/* > \endverbatim */
/* Authors: */
/* ======== */
/* > \author Univ. of Tennessee */
/* > \author Univ. of California Berkeley */
/* > \author Univ. of Colorado Denver */
/* > \author NAG Ltd. */
/* > \date November 2011 */
/* > \ingroup doubleOTHERcomputational */
/* > \par Further Details: */
/* ===================== */
/* > */
/* > \verbatim */
/* > */
/* > The reciprocal of the condition number of a generalized eigenvalue */
/* > w = (a, b) is defined as */
/* > */
/* > S(w) = (|u**TAv|**2 + |u**TBv|**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**TAv/u**TBv) */
/* > 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**T*(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**T*(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**T*S11*V1 = ( s11 s12 ) and U1**T*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**T * Z1 - lambda I), */
/* > where Z1**T denotes the 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**T, In-2) -kron(I2, S22) ] */
/* > [ kron(T11**T, 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. */
/* > \endverbatim */
/* > \par Contributors: */
/* ================== */
/* > */
/* > Bo Kagstrom and Peter Poromaa, Department of Computing Science, */
/* > Umea University, S-901 87 Umea, Sweden. */
/* > \par References: */
/* ================ */
/* > */
/* > \verbatim */
/* > */
/* > [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. */
/* > \endverbatim */
/* > */
/* ===================================================================== */
/* 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 computational routine (version 3.4.0) -- */
    /* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
    /* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
    /* November 2011 */
    /* .. Scalar Arguments .. */
    /* .. */
    /* .. Array Arguments .. */
    /* .. */
    /* ===================================================================== */
    /* .. 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); // , expr subst
                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_ */