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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 DSTEBZ
   *
   *  =========== DOCUMENTATION ===========
   *
   * Online html documentation available at 
   *            http://www.netlib.org/lapack/explore-html/ 
   *
   *> \htmlonly
   *> Download DSTEDC + dependencies 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dstedc.f"> 
   *> [TGZ]</a> 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dstedc.f"> 
   *> [ZIP]</a> 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dstedc.f"> 
   *> [TXT]</a>
   *> \endhtmlonly 
   *
   *  Definition:
   *  ===========
   *
   *       SUBROUTINE DSTEDC( COMPZ, N, D, E, Z, LDZ, WORK, LWORK, IWORK,
   *                          LIWORK, INFO )
   * 
   *       .. Scalar Arguments ..
   *       CHARACTER          COMPZ
   *       INTEGER            INFO, LDZ, LIWORK, LWORK, N
   *       ..
   *       .. Array Arguments ..
   *       INTEGER            IWORK( * )
   *       DOUBLE PRECISION   D( * ), E( * ), WORK( * ), Z( LDZ, * )
   *       ..
   *  
   *
   *> \par Purpose:
   *  =============
   *>
   *> \verbatim
   *>
   *> DSTEDC computes all eigenvalues and, optionally, eigenvectors of a
   *> symmetric tridiagonal matrix using the divide and conquer method.
   *> The eigenvectors of a full or band real symmetric matrix can also be
   *> found if DSYTRD or DSPTRD or DSBTRD has been used to reduce this
   *> matrix to tridiagonal form.
   *>
   *> This code makes very mild assumptions about floating point
   *> arithmetic. It will work on machines with a guard digit in
   *> add/subtract, or on those binary machines without guard digits
   *> which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or Cray-2.
   *> It could conceivably fail on hexadecimal or decimal machines
   *> without guard digits, but we know of none.  See DLAED3 for details.
   *> \endverbatim
   *
   *  Arguments:
   *  ==========
   *
   *> \param[in] COMPZ
   *> \verbatim
   *>          COMPZ is CHARACTER*1
   *>          = 'N':  Compute eigenvalues only.
   *>          = 'I':  Compute eigenvectors of tridiagonal matrix also.
   *>          = 'V':  Compute eigenvectors of original dense symmetric
   *>                  matrix also.  On entry, Z contains the orthogonal
   *>                  matrix used to reduce the original matrix to
   *>                  tridiagonal form.
   *> \endverbatim
   *>
   *> \param[in] N
   *> \verbatim
   *>          N is INTEGER
   *>          The dimension of the symmetric tridiagonal matrix.  N >= 0.
   *> \endverbatim
   *>
   *> \param[in,out] D
   *> \verbatim
   *>          D is DOUBLE PRECISION array, dimension (N)
   *>          On entry, the diagonal elements of the tridiagonal matrix.
   *>          On exit, if INFO = 0, the eigenvalues in ascending order.
   *> \endverbatim
   *>
   *> \param[in,out] E
   *> \verbatim
   *>          E is DOUBLE PRECISION array, dimension (N-1)
   *>          On entry, the subdiagonal elements of the tridiagonal matrix.
   *>          On exit, E has been destroyed.
   *> \endverbatim
   *>
   *> \param[in,out] Z
   *> \verbatim
   *>          Z is DOUBLE PRECISION array, dimension (LDZ,N)
   *>          On entry, if COMPZ = 'V', then Z contains the orthogonal
   *>          matrix used in the reduction to tridiagonal form.
   *>          On exit, if INFO = 0, then if COMPZ = 'V', Z contains the
   *>          orthonormal eigenvectors of the original symmetric matrix,
   *>          and if COMPZ = 'I', Z contains the orthonormal eigenvectors
   *>          of the symmetric tridiagonal matrix.
   *>          If  COMPZ = 'N', then Z is not referenced.
   *> \endverbatim
   *>
   *> \param[in] LDZ
   *> \verbatim
   *>          LDZ is INTEGER
   *>          The leading dimension of the array Z.  LDZ >= 1.
   *>          If eigenvectors are desired, then LDZ >= max(1,N).
   *> \endverbatim
   *>
   *> \param[out] WORK
   *> \verbatim
   *>          WORK is DOUBLE PRECISION array,
   *>                                         dimension (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.
   *>          If COMPZ = 'N' or N <= 1 then LWORK must be at least 1.
   *>          If COMPZ = 'V' and N > 1 then LWORK must be at least
   *>                         ( 1 + 3*N + 2*N*lg N + 4*N**2 ),
   *>                         where lg( N ) = smallest integer k such
   *>                         that 2**k >= N.
   *>          If COMPZ = 'I' and N > 1 then LWORK must be at least
   *>                         ( 1 + 4*N + N**2 ).
   *>          Note that for COMPZ = 'I' or 'V', then if N is less than or
   *>          equal to the minimum divide size, usually 25, then LWORK need
   *>          only be max(1,2*(N-1)).
   *>
   *>          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 (MAX(1,LIWORK))
   *>          On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK.
   *> \endverbatim
   *>
   *> \param[in] LIWORK
   *> \verbatim
   *>          LIWORK is INTEGER
   *>          The dimension of the array IWORK.
   *>          If COMPZ = 'N' or N <= 1 then LIWORK must be at least 1.
   *>          If COMPZ = 'V' and N > 1 then LIWORK must be at least
   *>                         ( 6 + 6*N + 5*N*lg N ).
   *>          If COMPZ = 'I' and N > 1 then LIWORK must be at least
   *>                         ( 3 + 5*N ).
   *>          Note that for COMPZ = 'I' or 'V', then if N is less than or
   *>          equal to the minimum divide size, usually 25, then LIWORK
   *>          need only be 1.
   *>
   *>          If LIWORK = -1, then a workspace query is assumed; the
   *>          routine only calculates the optimal size of the IWORK array,
   *>          returns this value as the first entry of the IWORK array, and
   *>          no error message related to LIWORK is issued by XERBLA.
   *> \endverbatim
   *>
   *> \param[out] INFO
   *> \verbatim
   *>          INFO is INTEGER
   *>          = 0:  successful exit.
   *>          < 0:  if INFO = -i, the i-th argument had an illegal value.
   *>          > 0:  The algorithm failed to compute an eigenvalue while
   *>                working on the submatrix lying in rows and columns
   *>                INFO/(N+1) through mod(INFO,N+1).
   *> \endverbatim
   *
   *  Authors:
   *  ========
   *
   *> \author Univ. of Tennessee 
   *> \author Univ. of California Berkeley 
   *> \author Univ. of Colorado Denver 
   *> \author NAG Ltd. 
   *
   *> \date November 2011
   *
   *> \ingroup auxOTHERcomputational
   *
   *> \par Contributors:
   *  ==================
   *>
   *> Jeff Rutter, Computer Science Division, University of California
   *> at Berkeley, USA \n
   *>  Modified by Francoise Tisseur, University of Tennessee
   *>
   *  =====================================================================
       SUBROUTINE DSTEDC( COMPZ, N, D, E, Z, LDZ, WORK, LWORK, IWORK,        SUBROUTINE DSTEDC( COMPZ, N, D, E, Z, LDZ, WORK, LWORK, IWORK,
      $                   LIWORK, INFO )       $                   LIWORK, INFO )
 *  *
 *  -- LAPACK driver 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          COMPZ        CHARACTER          COMPZ
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       DOUBLE PRECISION   D( * ), E( * ), WORK( * ), Z( LDZ, * )        DOUBLE PRECISION   D( * ), E( * ), WORK( * ), Z( LDZ, * )
 *     ..  *     ..
 *  *
 *  Purpose  
 *  =======  
 *  
 *  DSTEDC computes all eigenvalues and, optionally, eigenvectors of a  
 *  symmetric tridiagonal matrix using the divide and conquer method.  
 *  The eigenvectors of a full or band real symmetric matrix can also be  
 *  found if DSYTRD or DSPTRD or DSBTRD has been used to reduce this  
 *  matrix to tridiagonal form.  
 *  
 *  This code makes very mild assumptions about floating point  
 *  arithmetic. It will work on machines with a guard digit in  
 *  add/subtract, or on those binary machines without guard digits  
 *  which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or Cray-2.  
 *  It could conceivably fail on hexadecimal or decimal machines  
 *  without guard digits, but we know of none.  See DLAED3 for details.  
 *  
 *  Arguments  
 *  =========  
 *  
 *  COMPZ   (input) CHARACTER*1  
 *          = 'N':  Compute eigenvalues only.  
 *          = 'I':  Compute eigenvectors of tridiagonal matrix also.  
 *          = 'V':  Compute eigenvectors of original dense symmetric  
 *                  matrix also.  On entry, Z contains the orthogonal  
 *                  matrix used to reduce the original matrix to  
 *                  tridiagonal form.  
 *  
 *  N       (input) INTEGER  
 *          The dimension of the symmetric tridiagonal matrix.  N >= 0.  
 *  
 *  D       (input/output) DOUBLE PRECISION array, dimension (N)  
 *          On entry, the diagonal elements of the tridiagonal matrix.  
 *          On exit, if INFO = 0, the eigenvalues in ascending order.  
 *  
 *  E       (input/output) DOUBLE PRECISION array, dimension (N-1)  
 *          On entry, the subdiagonal elements of the tridiagonal matrix.  
 *          On exit, E has been destroyed.  
 *  
 *  Z       (input/output) DOUBLE PRECISION array, dimension (LDZ,N)  
 *          On entry, if COMPZ = 'V', then Z contains the orthogonal  
 *          matrix used in the reduction to tridiagonal form.  
 *          On exit, if INFO = 0, then if COMPZ = 'V', Z contains the  
 *          orthonormal eigenvectors of the original symmetric matrix,  
 *          and if COMPZ = 'I', Z contains the orthonormal eigenvectors  
 *          of the symmetric tridiagonal matrix.  
 *          If  COMPZ = 'N', then Z is not referenced.  
 *  
 *  LDZ     (input) INTEGER  
 *          The leading dimension of the array Z.  LDZ >= 1.  
 *          If eigenvectors are desired, then LDZ >= max(1,N).  
 *  
 *  WORK    (workspace/output) DOUBLE PRECISION array,  
 *                                         dimension (LWORK)  
 *          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.  
 *  
 *  LWORK   (input) INTEGER  
 *          The dimension of the array WORK.  
 *          If COMPZ = 'N' or N <= 1 then LWORK must be at least 1.  
 *          If COMPZ = 'V' and N > 1 then LWORK must be at least  
 *                         ( 1 + 3*N + 2*N*lg N + 3*N**2 ),  
 *                         where lg( N ) = smallest integer k such  
 *                         that 2**k >= N.  
 *          If COMPZ = 'I' and N > 1 then LWORK must be at least  
 *                         ( 1 + 4*N + N**2 ).  
 *          Note that for COMPZ = 'I' or 'V', then if N is less than or  
 *          equal to the minimum divide size, usually 25, then LWORK need  
 *          only be max(1,2*(N-1)).  
 *  
 *          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.  
 *  
 *  IWORK   (workspace/output) INTEGER array, dimension (MAX(1,LIWORK))  
 *          On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK.  
 *  
 *  LIWORK  (input) INTEGER  
 *          The dimension of the array IWORK.  
 *          If COMPZ = 'N' or N <= 1 then LIWORK must be at least 1.  
 *          If COMPZ = 'V' and N > 1 then LIWORK must be at least  
 *                         ( 6 + 6*N + 5*N*lg N ).  
 *          If COMPZ = 'I' and N > 1 then LIWORK must be at least  
 *                         ( 3 + 5*N ).  
 *          Note that for COMPZ = 'I' or 'V', then if N is less than or  
 *          equal to the minimum divide size, usually 25, then LIWORK  
 *          need only be 1.  
 *  
 *          If LIWORK = -1, then a workspace query is assumed; the  
 *          routine only calculates the optimal size of the IWORK array,  
 *          returns this value as the first entry of the IWORK array, and  
 *          no error message related to LIWORK is issued by XERBLA.  
 *  
 *  INFO    (output) INTEGER  
 *          = 0:  successful exit.  
 *          < 0:  if INFO = -i, the i-th argument had an illegal value.  
 *          > 0:  The algorithm failed to compute an eigenvalue while  
 *                working on the submatrix lying in rows and columns  
 *                INFO/(N+1) through mod(INFO,N+1).  
 *  
 *  Further Details  
 *  ===============  
 *  
 *  Based on contributions by  
 *     Jeff Rutter, Computer Science Division, University of California  
 *     at Berkeley, USA  
 *  Modified by Francoise Tisseur, University of Tennessee.  
 *  
 *  =====================================================================  *  =====================================================================
 *  *
 *     .. Parameters ..  *     .. Parameters ..
Line 190 Line 271
             IF( 2**LGN.LT.N )              IF( 2**LGN.LT.N )
      $         LGN = LGN + 1       $         LGN = LGN + 1
             IF( ICOMPZ.EQ.1 ) THEN              IF( ICOMPZ.EQ.1 ) THEN
                LWMIN = 1 + 3*N + 2*N*LGN + 3*N**2                 LWMIN = 1 + 3*N + 2*N*LGN + 4*N**2
                LIWMIN = 6 + 6*N + 5*N*LGN                 LIWMIN = 6 + 6*N + 5*N*LGN
             ELSE IF( ICOMPZ.EQ.2 ) THEN              ELSE IF( ICOMPZ.EQ.2 ) THEN
                LWMIN = 1 + 4*N + N**2                 LWMIN = 1 + 4*N + N**2
Removed from v.1.7  
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  Added in v.1.8

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