text: /* ../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_ */
  