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      SUBROUTINE <a name="STGSNA.1"></a><a href="stgsna.f.html#STGSNA.1">STGSNA</a>( JOB, HOWMNY, SELECT, N, A, LDA, B, LDB, VL,
     $                   LDVL, VR, LDVR, S, DIF, MM, M, WORK, LWORK,
     $                   IWORK, INFO )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  -- LAPACK routine (version 3.1) --
</span><span class="comment">*</span><span class="comment">     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
</span><span class="comment">*</span><span class="comment">     November 2006
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">     .. Scalar Arguments ..
</span>      CHARACTER          HOWMNY, JOB
      INTEGER            INFO, LDA, LDB, LDVL, LDVR, LWORK, M, MM, N
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">     .. Array Arguments ..
</span>      LOGICAL            SELECT( * )
      INTEGER            IWORK( * )
      REAL               A( LDA, * ), B( LDB, * ), DIF( * ), S( * ),
     $                   VL( LDVL, * ), VR( LDVR, * ), WORK( * )
<span class="comment">*</span><span class="comment">     ..
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  Purpose
</span><span class="comment">*</span><span class="comment">  =======
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  <a name="STGSNA.23"></a><a href="stgsna.f.html#STGSNA.1">STGSNA</a> estimates reciprocal condition numbers for specified
</span><span class="comment">*</span><span class="comment">  eigenvalues and/or eigenvectors of a matrix pair (A, B) in
</span><span class="comment">*</span><span class="comment">  generalized real Schur canonical form (or of any matrix pair
</span><span class="comment">*</span><span class="comment">  (Q*A*Z', Q*B*Z') with orthogonal matrices Q and Z, where
</span><span class="comment">*</span><span class="comment">  Z' denotes the transpose of Z.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  (A, B) must be in generalized real Schur form (as returned by <a name="SGGES.29"></a><a href="sgges.f.html#SGGES.1">SGGES</a>),
</span><span class="comment">*</span><span class="comment">  i.e. A is block upper triangular with 1-by-1 and 2-by-2 diagonal
</span><span class="comment">*</span><span class="comment">  blocks. B is upper triangular.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  Arguments
</span><span class="comment">*</span><span class="comment">  =========
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  JOB     (input) CHARACTER*1
</span><span class="comment">*</span><span class="comment">          Specifies whether condition numbers are required for
</span><span class="comment">*</span><span class="comment">          eigenvalues (S) or eigenvectors (DIF):
</span><span class="comment">*</span><span class="comment">          = 'E': for eigenvalues only (S);
</span><span class="comment">*</span><span class="comment">          = 'V': for eigenvectors only (DIF);
</span><span class="comment">*</span><span class="comment">          = 'B': for both eigenvalues and eigenvectors (S and DIF).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  HOWMNY  (input) CHARACTER*1
</span><span class="comment">*</span><span class="comment">          = 'A': compute condition numbers for all eigenpairs;
</span><span class="comment">*</span><span class="comment">          = 'S': compute condition numbers for selected eigenpairs
</span><span class="comment">*</span><span class="comment">                 specified by the array SELECT.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  SELECT  (input) LOGICAL array, dimension (N)
</span><span class="comment">*</span><span class="comment">          If HOWMNY = 'S', SELECT specifies the eigenpairs for which
</span><span class="comment">*</span><span class="comment">          condition numbers are required. To select condition numbers
</span><span class="comment">*</span><span class="comment">          for the eigenpair corresponding to a real eigenvalue w(j),
</span><span class="comment">*</span><span class="comment">          SELECT(j) must be set to .TRUE.. To select condition numbers
</span><span class="comment">*</span><span class="comment">          corresponding to a complex conjugate pair of eigenvalues w(j)
</span><span class="comment">*</span><span class="comment">          and w(j+1), either SELECT(j) or SELECT(j+1) or both, must be
</span><span class="comment">*</span><span class="comment">          set to .TRUE..
</span><span class="comment">*</span><span class="comment">          If HOWMNY = 'A', SELECT is not referenced.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  N       (input) INTEGER
</span><span class="comment">*</span><span class="comment">          The order of the square matrix pair (A, B). N &gt;= 0.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  A       (input) REAL array, dimension (LDA,N)
</span><span class="comment">*</span><span class="comment">          The upper quasi-triangular matrix A in the pair (A,B).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  LDA     (input) INTEGER
</span><span class="comment">*</span><span class="comment">          The leading dimension of the array A. LDA &gt;= max(1,N).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  B       (input) REAL array, dimension (LDB,N)
</span><span class="comment">*</span><span class="comment">          The upper triangular matrix B in the pair (A,B).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  LDB     (input) INTEGER
</span><span class="comment">*</span><span class="comment">          The leading dimension of the array B. LDB &gt;= max(1,N).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  VL      (input) REAL array, dimension (LDVL,M)
</span><span class="comment">*</span><span class="comment">          If JOB = 'E' or 'B', VL must contain left eigenvectors of
</span><span class="comment">*</span><span class="comment">          (A, B), corresponding to the eigenpairs specified by HOWMNY
</span><span class="comment">*</span><span class="comment">          and SELECT. The eigenvectors must be stored in consecutive
</span><span class="comment">*</span><span class="comment">          columns of VL, as returned by <a name="STGEVC.78"></a><a href="stgevc.f.html#STGEVC.1">STGEVC</a>.
</span><span class="comment">*</span><span class="comment">          If JOB = 'V', VL is not referenced.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  LDVL    (input) INTEGER
</span><span class="comment">*</span><span class="comment">          The leading dimension of the array VL. LDVL &gt;= 1.
</span><span class="comment">*</span><span class="comment">          If JOB = 'E' or 'B', LDVL &gt;= N.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  VR      (input) REAL array, dimension (LDVR,M)
</span><span class="comment">*</span><span class="comment">          If JOB = 'E' or 'B', VR must contain right eigenvectors of
</span><span class="comment">*</span><span class="comment">          (A, B), corresponding to the eigenpairs specified by HOWMNY
</span><span class="comment">*</span><span class="comment">          and SELECT. The eigenvectors must be stored in consecutive
</span><span class="comment">*</span><span class="comment">          columns ov VR, as returned by <a name="STGEVC.89"></a><a href="stgevc.f.html#STGEVC.1">STGEVC</a>.
</span><span class="comment">*</span><span class="comment">          If JOB = 'V', VR is not referenced.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  LDVR    (input) INTEGER
</span><span class="comment">*</span><span class="comment">          The leading dimension of the array VR. LDVR &gt;= 1.
</span><span class="comment">*</span><span class="comment">          If JOB = 'E' or 'B', LDVR &gt;= N.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  S       (output) REAL array, dimension (MM)
</span><span class="comment">*</span><span class="comment">          If JOB = 'E' or 'B', the reciprocal condition numbers of the
</span><span class="comment">*</span><span class="comment">          selected eigenvalues, stored in consecutive elements of the
</span><span class="comment">*</span><span class="comment">          array. For a complex conjugate pair of eigenvalues two
</span><span class="comment">*</span><span class="comment">          consecutive elements of S are set to the same value. Thus
</span><span class="comment">*</span><span class="comment">          S(j), DIF(j), and the j-th columns of VL and VR all
</span><span class="comment">*</span><span class="comment">          correspond to the same eigenpair (but not in general the
</span><span class="comment">*</span><span class="comment">          j-th eigenpair, unless all eigenpairs are selected).
</span><span class="comment">*</span><span class="comment">          If JOB = 'V', S is not referenced.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  DIF     (output) REAL array, dimension (MM)
</span><span class="comment">*</span><span class="comment">          If JOB = 'V' or 'B', the estimated reciprocal condition
</span><span class="comment">*</span><span class="comment">          numbers of the selected eigenvectors, stored in consecutive
</span><span class="comment">*</span><span class="comment">          elements of the array. For a complex eigenvector two
</span><span class="comment">*</span><span class="comment">          consecutive elements of DIF are set to the same value. If
</span><span class="comment">*</span><span class="comment">          the eigenvalues cannot be reordered to compute DIF(j), DIF(j)
</span><span class="comment">*</span><span class="comment">          is set to 0; this can only occur when the true value would be
</span><span class="comment">*</span><span class="comment">          very small anyway.
</span><span class="comment">*</span><span class="comment">          If JOB = 'E', DIF is not referenced.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  MM      (input) INTEGER
</span><span class="comment">*</span><span class="comment">          The number of elements in the arrays S and DIF. MM &gt;= M.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  M       (output) INTEGER
</span><span class="comment">*</span><span class="comment">          The number of elements of the arrays S and DIF used to store
</span><span class="comment">*</span><span class="comment">          the specified condition numbers; for each selected real
</span><span class="comment">*</span><span class="comment">          eigenvalue one element is used, and for each selected complex
</span><span class="comment">*</span><span class="comment">          conjugate pair of eigenvalues, two elements are used.
</span><span class="comment">*</span><span class="comment">          If HOWMNY = 'A', M is set to N.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  WORK    (workspace/output) REAL array, dimension (MAX(1,LWORK))
</span><span class="comment">*</span><span class="comment">          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  LWORK   (input) INTEGER
</span><span class="comment">*</span><span class="comment">          The dimension of the array WORK. LWORK &gt;= max(1,N).
</span><span class="comment">*</span><span class="comment">          If JOB = 'V' or 'B' LWORK &gt;= 2*N*(N+2)+16.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">          If LWORK = -1, then a workspace query is assumed; the routine
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