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version 1.7, 2010/12/21 13:53:38 version 1.8, 2011/11/21 20:43:04
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   *> \brief \b DSTEIN
   *
   *  =========== DOCUMENTATION ===========
   *
   * Online html documentation available at 
   *            http://www.netlib.org/lapack/explore-html/ 
   *
   *> \htmlonly
   *> Download DSTEIN + dependencies 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dstein.f"> 
   *> [TGZ]</a> 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dstein.f"> 
   *> [ZIP]</a> 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dstein.f"> 
   *> [TXT]</a>
   *> \endhtmlonly 
   *
   *  Definition:
   *  ===========
   *
   *       SUBROUTINE DSTEIN( N, D, E, M, W, IBLOCK, ISPLIT, Z, LDZ, WORK,
   *                          IWORK, IFAIL, INFO )
   * 
   *       .. Scalar Arguments ..
   *       INTEGER            INFO, LDZ, M, N
   *       ..
   *       .. Array Arguments ..
   *       INTEGER            IBLOCK( * ), IFAIL( * ), ISPLIT( * ),
   *      $                   IWORK( * )
   *       DOUBLE PRECISION   D( * ), E( * ), W( * ), WORK( * ), Z( LDZ, * )
   *       ..
   *  
   *
   *> \par Purpose:
   *  =============
   *>
   *> \verbatim
   *>
   *> DSTEIN computes the eigenvectors of a real symmetric tridiagonal
   *> matrix T corresponding to specified eigenvalues, using inverse
   *> iteration.
   *>
   *> The maximum number of iterations allowed for each eigenvector is
   *> specified by an internal parameter MAXITS (currently set to 5).
   *> \endverbatim
   *
   *  Arguments:
   *  ==========
   *
   *> \param[in] N
   *> \verbatim
   *>          N is INTEGER
   *>          The order of the matrix.  N >= 0.
   *> \endverbatim
   *>
   *> \param[in] D
   *> \verbatim
   *>          D is DOUBLE PRECISION array, dimension (N)
   *>          The n diagonal elements of the tridiagonal matrix T.
   *> \endverbatim
   *>
   *> \param[in] E
   *> \verbatim
   *>          E is DOUBLE PRECISION array, dimension (N-1)
   *>          The (n-1) subdiagonal elements of the tridiagonal matrix
   *>          T, in elements 1 to N-1.
   *> \endverbatim
   *>
   *> \param[in] M
   *> \verbatim
   *>          M is INTEGER
   *>          The number of eigenvectors to be found.  0 <= M <= N.
   *> \endverbatim
   *>
   *> \param[in] W
   *> \verbatim
   *>          W is DOUBLE PRECISION array, dimension (N)
   *>          The first M elements of W contain the eigenvalues for
   *>          which eigenvectors are to be computed.  The eigenvalues
   *>          should be grouped by split-off block and ordered from
   *>          smallest to largest within the block.  ( The output array
   *>          W from DSTEBZ with ORDER = 'B' is expected here. )
   *> \endverbatim
   *>
   *> \param[in] IBLOCK
   *> \verbatim
   *>          IBLOCK is INTEGER array, dimension (N)
   *>          The submatrix indices associated with the corresponding
   *>          eigenvalues in W; IBLOCK(i)=1 if eigenvalue W(i) belongs to
   *>          the first submatrix from the top, =2 if W(i) belongs to
   *>          the second submatrix, etc.  ( The output array IBLOCK
   *>          from DSTEBZ is expected here. )
   *> \endverbatim
   *>
   *> \param[in] ISPLIT
   *> \verbatim
   *>          ISPLIT is INTEGER array, dimension (N)
   *>          The splitting points, at which T breaks up into submatrices.
   *>          The first submatrix consists of rows/columns 1 to
   *>          ISPLIT( 1 ), the second of rows/columns ISPLIT( 1 )+1
   *>          through ISPLIT( 2 ), etc.
   *>          ( The output array ISPLIT from DSTEBZ is expected here. )
   *> \endverbatim
   *>
   *> \param[out] Z
   *> \verbatim
   *>          Z is DOUBLE PRECISION array, dimension (LDZ, M)
   *>          The computed eigenvectors.  The eigenvector associated
   *>          with the eigenvalue W(i) is stored in the i-th column of
   *>          Z.  Any vector which fails to converge is set to its current
   *>          iterate after MAXITS iterations.
   *> \endverbatim
   *>
   *> \param[in] LDZ
   *> \verbatim
   *>          LDZ is INTEGER
   *>          The leading dimension of the array Z.  LDZ >= max(1,N).
   *> \endverbatim
   *>
   *> \param[out] WORK
   *> \verbatim
   *>          WORK is DOUBLE PRECISION array, dimension (5*N)
   *> \endverbatim
   *>
   *> \param[out] IWORK
   *> \verbatim
   *>          IWORK is INTEGER array, dimension (N)
   *> \endverbatim
   *>
   *> \param[out] IFAIL
   *> \verbatim
   *>          IFAIL is INTEGER array, dimension (M)
   *>          On normal exit, all elements of IFAIL are zero.
   *>          If one or more eigenvectors fail to converge after
   *>          MAXITS iterations, then their indices are stored in
   *>          array IFAIL.
   *> \endverbatim
   *>
   *> \param[out] INFO
   *> \verbatim
   *>          INFO is INTEGER
   *>          = 0: successful exit.
   *>          < 0: if INFO = -i, the i-th argument had an illegal value
   *>          > 0: if INFO = i, then i eigenvectors failed to converge
   *>               in MAXITS iterations.  Their indices are stored in
   *>               array IFAIL.
   *> \endverbatim
   *
   *> \par Internal Parameters:
   *  =========================
   *>
   *> \verbatim
   *>  MAXITS  INTEGER, default = 5
   *>          The maximum number of iterations performed.
   *>
   *>  EXTRA   INTEGER, default = 2
   *>          The number of iterations performed after norm growth
   *>          criterion is satisfied, should be at least 1.
   *> \endverbatim
   *
   *  Authors:
   *  ========
   *
   *> \author Univ. of Tennessee 
   *> \author Univ. of California Berkeley 
   *> \author Univ. of Colorado Denver 
   *> \author NAG Ltd. 
   *
   *> \date November 2011
   *
   *> \ingroup doubleOTHERcomputational
   *
   *  =====================================================================
       SUBROUTINE DSTEIN( N, D, E, M, W, IBLOCK, ISPLIT, Z, LDZ, WORK,        SUBROUTINE DSTEIN( N, D, E, M, W, IBLOCK, ISPLIT, Z, LDZ, WORK,
      $                   IWORK, IFAIL, INFO )       $                   IWORK, IFAIL, 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 ..
       INTEGER            INFO, LDZ, M, N        INTEGER            INFO, LDZ, M, N
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       DOUBLE PRECISION   D( * ), E( * ), W( * ), WORK( * ), Z( LDZ, * )        DOUBLE PRECISION   D( * ), E( * ), W( * ), WORK( * ), Z( LDZ, * )
 *     ..  *     ..
 *  *
 *  Purpose  
 *  =======  
 *  
 *  DSTEIN computes the eigenvectors of a real symmetric tridiagonal  
 *  matrix T corresponding to specified eigenvalues, using inverse  
 *  iteration.  
 *  
 *  The maximum number of iterations allowed for each eigenvector is  
 *  specified by an internal parameter MAXITS (currently set to 5).  
 *  
 *  Arguments  
 *  =========  
 *  
 *  N       (input) INTEGER  
 *          The order of the matrix.  N >= 0.  
 *  
 *  D       (input) DOUBLE PRECISION array, dimension (N)  
 *          The n diagonal elements of the tridiagonal matrix T.  
 *  
 *  E       (input) DOUBLE PRECISION array, dimension (N-1)  
 *          The (n-1) subdiagonal elements of the tridiagonal matrix  
 *          T, in elements 1 to N-1.  
 *  
 *  M       (input) INTEGER  
 *          The number of eigenvectors to be found.  0 <= M <= N.  
 *  
 *  W       (input) DOUBLE PRECISION array, dimension (N)  
 *          The first M elements of W contain the eigenvalues for  
 *          which eigenvectors are to be computed.  The eigenvalues  
 *          should be grouped by split-off block and ordered from  
 *          smallest to largest within the block.  ( The output array  
 *          W from DSTEBZ with ORDER = 'B' is expected here. )  
 *  
 *  IBLOCK  (input) INTEGER array, dimension (N)  
 *          The submatrix indices associated with the corresponding  
 *          eigenvalues in W; IBLOCK(i)=1 if eigenvalue W(i) belongs to  
 *          the first submatrix from the top, =2 if W(i) belongs to  
 *          the second submatrix, etc.  ( The output array IBLOCK  
 *          from DSTEBZ is expected here. )  
 *  
 *  ISPLIT  (input) INTEGER array, dimension (N)  
 *          The splitting points, at which T breaks up into submatrices.  
 *          The first submatrix consists of rows/columns 1 to  
 *          ISPLIT( 1 ), the second of rows/columns ISPLIT( 1 )+1  
 *          through ISPLIT( 2 ), etc.  
 *          ( The output array ISPLIT from DSTEBZ is expected here. )  
 *  
 *  Z       (output) DOUBLE PRECISION array, dimension (LDZ, M)  
 *          The computed eigenvectors.  The eigenvector associated  
 *          with the eigenvalue W(i) is stored in the i-th column of  
 *          Z.  Any vector which fails to converge is set to its current  
 *          iterate after MAXITS iterations.  
 *  
 *  LDZ     (input) INTEGER  
 *          The leading dimension of the array Z.  LDZ >= max(1,N).  
 *  
 *  WORK    (workspace) DOUBLE PRECISION array, dimension (5*N)  
 *  
 *  IWORK   (workspace) INTEGER array, dimension (N)  
 *  
 *  IFAIL   (output) INTEGER array, dimension (M)  
 *          On normal exit, all elements of IFAIL are zero.  
 *          If one or more eigenvectors fail to converge after  
 *          MAXITS iterations, then their indices are stored in  
 *          array IFAIL.  
 *  
 *  INFO    (output) INTEGER  
 *          = 0: successful exit.  
 *          < 0: if INFO = -i, the i-th argument had an illegal value  
 *          > 0: if INFO = i, then i eigenvectors failed to converge  
 *               in MAXITS iterations.  Their indices are stored in  
 *               array IFAIL.  
 *  
 *  Internal Parameters  
 *  ===================  
 *  
 *  MAXITS  INTEGER, default = 5  
 *          The maximum number of iterations performed.  
 *  
 *  EXTRA   INTEGER, default = 2  
 *          The number of iterations performed after norm growth  
 *          criterion is satisfied, should be at least 1.  
 *  
 *  =====================================================================  *  =====================================================================
 *  *
 *     .. Parameters ..  *     .. Parameters ..
Removed from v.1.7  
changed lines
  Added in v.1.8

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