ctgsna.f.html

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      SUBROUTINE <a name="CTGSNA.1"></a><a href="ctgsna.f.html#CTGSNA.1">CTGSNA</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               DIF( * ), S( * )
      COMPLEX            A( LDA, * ), B( LDB, * ), 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="CTGSNA.24"></a><a href="ctgsna.f.html#CTGSNA.1">CTGSNA</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).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  (A, B) must be in generalized Schur canonical form, that is, A and
</span><span class="comment">*</span><span class="comment">  B are both upper triangular.
</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 corresponding j-th eigenvalue and/or eigenvector,
</span><span class="comment">*</span><span class="comment">          SELECT(j) must be 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) COMPLEX array, dimension (LDA,N)
</span><span class="comment">*</span><span class="comment">          The upper 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) COMPLEX 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) COMPLEX 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="CTGEVC.71"></a><a href="ctgevc.f.html#CTGEVC.1">CTGEVC</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; and
</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) COMPLEX 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 of VR, as returned by <a name="CTGEVC.82"></a><a href="ctgevc.f.html#CTGEVC.1">CTGEVC</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.
</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.
</span><span class="comment">*</span><span class="comment">          If the eigenvalues cannot be reordered to compute DIF(j),
</span><span class="comment">*</span><span class="comment">          DIF(j) is set to 0; this can only occur when the true value
</span><span class="comment">*</span><span class="comment">          would be very small anyway.
</span><span class="comment">*</span><span class="comment">          For each eigenvalue/vector specified by SELECT, DIF stores
</span><span class="comment">*</span><span class="comment">          a Frobenius norm-based estimate of Difl.
</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 eigenvalue
</span><span class="comment">*</span><span class="comment">          one element is used. 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) COMPLEX 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;= max(1,2*N*N).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">  IWORK   (workspace) INTEGER array, dimension (N+2)
</span><span class="comment">*</span><span class="comment">          If JOB = 'E', IWORK is not referenced.
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