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version 1.7, 2010/12/21 13:53:24 version 1.8, 2011/11/21 20:42:49
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   *> \brief \b DDISNA
   *
   *  =========== DOCUMENTATION ===========
   *
   * Online html documentation available at 
   *            http://www.netlib.org/lapack/explore-html/ 
   *
   *> \htmlonly
   *> Download DDISNA + dependencies 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/ddisna.f"> 
   *> [TGZ]</a> 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/ddisna.f"> 
   *> [ZIP]</a> 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/ddisna.f"> 
   *> [TXT]</a>
   *> \endhtmlonly 
   *
   *  Definition:
   *  ===========
   *
   *       SUBROUTINE DDISNA( JOB, M, N, D, SEP, INFO )
   * 
   *       .. Scalar Arguments ..
   *       CHARACTER          JOB
   *       INTEGER            INFO, M, N
   *       ..
   *       .. Array Arguments ..
   *       DOUBLE PRECISION   D( * ), SEP( * )
   *       ..
   *  
   *
   *> \par Purpose:
   *  =============
   *>
   *> \verbatim
   *>
   *> DDISNA computes the reciprocal condition numbers for the eigenvectors
   *> of a real symmetric or complex Hermitian matrix or for the left or
   *> right singular vectors of a general m-by-n matrix. The reciprocal
   *> condition number is the 'gap' between the corresponding eigenvalue or
   *> singular value and the nearest other one.
   *>
   *> The bound on the error, measured by angle in radians, in the I-th
   *> computed vector is given by
   *>
   *>        DLAMCH( 'E' ) * ( ANORM / SEP( I ) )
   *>
   *> where ANORM = 2-norm(A) = max( abs( D(j) ) ).  SEP(I) is not allowed
   *> to be smaller than DLAMCH( 'E' )*ANORM in order to limit the size of
   *> the error bound.
   *>
   *> DDISNA may also be used to compute error bounds for eigenvectors of
   *> the generalized symmetric definite eigenproblem.
   *> \endverbatim
   *
   *  Arguments:
   *  ==========
   *
   *> \param[in] JOB
   *> \verbatim
   *>          JOB is CHARACTER*1
   *>          Specifies for which problem the reciprocal condition numbers
   *>          should be computed:
   *>          = 'E':  the eigenvectors of a symmetric/Hermitian matrix;
   *>          = 'L':  the left singular vectors of a general matrix;
   *>          = 'R':  the right singular vectors of a general matrix.
   *> \endverbatim
   *>
   *> \param[in] M
   *> \verbatim
   *>          M is INTEGER
   *>          The number of rows of the matrix. M >= 0.
   *> \endverbatim
   *>
   *> \param[in] N
   *> \verbatim
   *>          N is INTEGER
   *>          If JOB = 'L' or 'R', the number of columns of the matrix,
   *>          in which case N >= 0. Ignored if JOB = 'E'.
   *> \endverbatim
   *>
   *> \param[in] D
   *> \verbatim
   *>          D is DOUBLE PRECISION array, dimension (M) if JOB = 'E'
   *>                              dimension (min(M,N)) if JOB = 'L' or 'R'
   *>          The eigenvalues (if JOB = 'E') or singular values (if JOB =
   *>          'L' or 'R') of the matrix, in either increasing or decreasing
   *>          order. If singular values, they must be non-negative.
   *> \endverbatim
   *>
   *> \param[out] SEP
   *> \verbatim
   *>          SEP is DOUBLE PRECISION array, dimension (M) if JOB = 'E'
   *>                               dimension (min(M,N)) if JOB = 'L' or 'R'
   *>          The reciprocal condition numbers of the vectors.
   *> \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 auxOTHERcomputational
   *
   *  =====================================================================
       SUBROUTINE DDISNA( JOB, M, N, D, SEP, INFO )        SUBROUTINE DDISNA( JOB, M, N, D, SEP, INFO )
 *  *
 *  -- LAPACK routine (version 3.2) --  *  -- LAPACK computational routine (version 3.4.0) --
 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --  *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--  *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
 *     November 2006  *     November 2011
 *  *
 *     .. Scalar Arguments ..  *     .. Scalar Arguments ..
       CHARACTER          JOB        CHARACTER          JOB
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       DOUBLE PRECISION   D( * ), SEP( * )        DOUBLE PRECISION   D( * ), SEP( * )
 *     ..  *     ..
 *  *
 *  Purpose  
 *  =======  
 *  
 *  DDISNA computes the reciprocal condition numbers for the eigenvectors  
 *  of a real symmetric or complex Hermitian matrix or for the left or  
 *  right singular vectors of a general m-by-n matrix. The reciprocal  
 *  condition number is the 'gap' between the corresponding eigenvalue or  
 *  singular value and the nearest other one.  
 *  
 *  The bound on the error, measured by angle in radians, in the I-th  
 *  computed vector is given by  
 *  
 *         DLAMCH( 'E' ) * ( ANORM / SEP( I ) )  
 *  
 *  where ANORM = 2-norm(A) = max( abs( D(j) ) ).  SEP(I) is not allowed  
 *  to be smaller than DLAMCH( 'E' )*ANORM in order to limit the size of  
 *  the error bound.  
 *  
 *  DDISNA may also be used to compute error bounds for eigenvectors of  
 *  the generalized symmetric definite eigenproblem.  
 *  
 *  Arguments  
 *  =========  
 *  
 *  JOB     (input) CHARACTER*1  
 *          Specifies for which problem the reciprocal condition numbers  
 *          should be computed:  
 *          = 'E':  the eigenvectors of a symmetric/Hermitian matrix;  
 *          = 'L':  the left singular vectors of a general matrix;  
 *          = 'R':  the right singular vectors of a general matrix.  
 *  
 *  M       (input) INTEGER  
 *          The number of rows of the matrix. M >= 0.  
 *  
 *  N       (input) INTEGER  
 *          If JOB = 'L' or 'R', the number of columns of the matrix,  
 *          in which case N >= 0. Ignored if JOB = 'E'.  
 *  
 *  D       (input) DOUBLE PRECISION array, dimension (M) if JOB = 'E'  
 *                              dimension (min(M,N)) if JOB = 'L' or 'R'  
 *          The eigenvalues (if JOB = 'E') or singular values (if JOB =  
 *          'L' or 'R') of the matrix, in either increasing or decreasing  
 *          order. If singular values, they must be non-negative.  
 *  
 *  SEP     (output) DOUBLE PRECISION array, dimension (M) if JOB = 'E'  
 *                               dimension (min(M,N)) if JOB = 'L' or 'R'  
 *          The reciprocal condition numbers of the vectors.  
 *  
 *  INFO    (output) INTEGER  
 *          = 0:  successful exit.  
 *          < 0:  if INFO = -i, the i-th argument had an illegal value.  
 *  
 *  =====================================================================  *  =====================================================================
 *  *
 *     .. Parameters ..  *     .. Parameters ..
Removed from v.1.7  
changed lines
  Added in v.1.8

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