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version 1.2, 2010/04/21 13:45:16 version 1.18, 2023/08/07 08:38:53
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   *> \brief \b DLAED0 used by DSTEDC. Computes all eigenvalues and corresponding eigenvectors of an unreduced symmetric tridiagonal matrix using the divide and conquer method.
   *
   *  =========== DOCUMENTATION ===========
   *
   * Online html documentation available at
   *            http://www.netlib.org/lapack/explore-html/
   *
   *> \htmlonly
   *> Download DLAED0 + dependencies
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlaed0.f">
   *> [TGZ]</a>
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlaed0.f">
   *> [ZIP]</a>
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlaed0.f">
   *> [TXT]</a>
   *> \endhtmlonly
   *
   *  Definition:
   *  ===========
   *
   *       SUBROUTINE DLAED0( ICOMPQ, QSIZ, N, D, E, Q, LDQ, QSTORE, LDQS,
   *                          WORK, IWORK, INFO )
   *
   *       .. Scalar Arguments ..
   *       INTEGER            ICOMPQ, INFO, LDQ, LDQS, N, QSIZ
   *       ..
   *       .. Array Arguments ..
   *       INTEGER            IWORK( * )
   *       DOUBLE PRECISION   D( * ), E( * ), Q( LDQ, * ), QSTORE( LDQS, * ),
   *      $                   WORK( * )
   *       ..
   *
   *
   *> \par Purpose:
   *  =============
   *>
   *> \verbatim
   *>
   *> DLAED0 computes all eigenvalues and corresponding eigenvectors of a
   *> symmetric tridiagonal matrix using the divide and conquer method.
   *> \endverbatim
   *
   *  Arguments:
   *  ==========
   *
   *> \param[in] ICOMPQ
   *> \verbatim
   *>          ICOMPQ is INTEGER
   *>          = 0:  Compute eigenvalues only.
   *>          = 1:  Compute eigenvectors of original dense symmetric matrix
   *>                also.  On entry, Q contains the orthogonal matrix used
   *>                to reduce the original matrix to tridiagonal form.
   *>          = 2:  Compute eigenvalues and eigenvectors of tridiagonal
   *>                matrix.
   *> \endverbatim
   *>
   *> \param[in] QSIZ
   *> \verbatim
   *>          QSIZ is INTEGER
   *>         The dimension of the orthogonal matrix used to reduce
   *>         the full matrix to tridiagonal form.  QSIZ >= N if ICOMPQ = 1.
   *> \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 main diagonal of the tridiagonal matrix.
   *>         On exit, its eigenvalues.
   *> \endverbatim
   *>
   *> \param[in] E
   *> \verbatim
   *>          E is DOUBLE PRECISION array, dimension (N-1)
   *>         The off-diagonal elements of the tridiagonal matrix.
   *>         On exit, E has been destroyed.
   *> \endverbatim
   *>
   *> \param[in,out] Q
   *> \verbatim
   *>          Q is DOUBLE PRECISION array, dimension (LDQ, N)
   *>         On entry, Q must contain an N-by-N orthogonal matrix.
   *>         If ICOMPQ = 0    Q is not referenced.
   *>         If ICOMPQ = 1    On entry, Q is a subset of the columns of the
   *>                          orthogonal matrix used to reduce the full
   *>                          matrix to tridiagonal form corresponding to
   *>                          the subset of the full matrix which is being
   *>                          decomposed at this time.
   *>         If ICOMPQ = 2    On entry, Q will be the identity matrix.
   *>                          On exit, Q contains the eigenvectors of the
   *>                          tridiagonal matrix.
   *> \endverbatim
   *>
   *> \param[in] LDQ
   *> \verbatim
   *>          LDQ is INTEGER
   *>         The leading dimension of the array Q.  If eigenvectors are
   *>         desired, then  LDQ >= max(1,N).  In any case,  LDQ >= 1.
   *> \endverbatim
   *>
   *> \param[out] QSTORE
   *> \verbatim
   *>          QSTORE is DOUBLE PRECISION array, dimension (LDQS, N)
   *>         Referenced only when ICOMPQ = 1.  Used to store parts of
   *>         the eigenvector matrix when the updating matrix multiplies
   *>         take place.
   *> \endverbatim
   *>
   *> \param[in] LDQS
   *> \verbatim
   *>          LDQS is INTEGER
   *>         The leading dimension of the array QSTORE.  If ICOMPQ = 1,
   *>         then  LDQS >= max(1,N).  In any case,  LDQS >= 1.
   *> \endverbatim
   *>
   *> \param[out] WORK
   *> \verbatim
   *>          WORK is DOUBLE PRECISION array,
   *>         If ICOMPQ = 0 or 1, the dimension of WORK must be at least
   *>                     1 + 3*N + 2*N*lg N + 3*N**2
   *>                     ( lg( N ) = smallest integer k
   *>                                 such that 2^k >= N )
   *>         If ICOMPQ = 2, the dimension of WORK must be at least
   *>                     4*N + N**2.
   *> \endverbatim
   *>
   *> \param[out] IWORK
   *> \verbatim
   *>          IWORK is INTEGER array,
   *>         If ICOMPQ = 0 or 1, the dimension of IWORK must be at least
   *>                        6 + 6*N + 5*N*lg N.
   *>                        ( lg( N ) = smallest integer k
   *>                                    such that 2^k >= N )
   *>         If ICOMPQ = 2, the dimension of IWORK must be at least
   *>                        3 + 5*N.
   *> \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.
   *
   *> \ingroup auxOTHERcomputational
   *
   *> \par Contributors:
   *  ==================
   *>
   *> Jeff Rutter, Computer Science Division, University of California
   *> at Berkeley, USA
   *
   *  =====================================================================
       SUBROUTINE DLAED0( ICOMPQ, QSIZ, N, D, E, Q, LDQ, QSTORE, LDQS,        SUBROUTINE DLAED0( ICOMPQ, QSIZ, N, D, E, Q, LDQ, QSTORE, LDQS,
      $                   WORK, IWORK, INFO )       $                   WORK, IWORK, INFO )
 *  *
 *  -- LAPACK routine (version 3.2) --  *  -- LAPACK computational routine --
 *  -- 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  
 *  *
 *     .. Scalar Arguments ..  *     .. Scalar Arguments ..
       INTEGER            ICOMPQ, INFO, LDQ, LDQS, N, QSIZ        INTEGER            ICOMPQ, INFO, LDQ, LDQS, N, QSIZ
Line 15 Line 183
      $                   WORK( * )       $                   WORK( * )
 *     ..  *     ..
 *  *
 *  Purpose  
 *  =======  
 *  
 *  DLAED0 computes all eigenvalues and corresponding eigenvectors of a  
 *  symmetric tridiagonal matrix using the divide and conquer method.  
 *  
 *  Arguments  
 *  =========  
 *  
 *  ICOMPQ  (input) INTEGER  
 *          = 0:  Compute eigenvalues only.  
 *          = 1:  Compute eigenvectors of original dense symmetric matrix  
 *                also.  On entry, Q contains the orthogonal matrix used  
 *                to reduce the original matrix to tridiagonal form.  
 *          = 2:  Compute eigenvalues and eigenvectors of tridiagonal  
 *                matrix.  
 *  
 *  QSIZ   (input) INTEGER  
 *         The dimension of the orthogonal matrix used to reduce  
 *         the full matrix to tridiagonal form.  QSIZ >= N if ICOMPQ = 1.  
 *  
 *  N      (input) INTEGER  
 *         The dimension of the symmetric tridiagonal matrix.  N >= 0.  
 *  
 *  D      (input/output) DOUBLE PRECISION array, dimension (N)  
 *         On entry, the main diagonal of the tridiagonal matrix.  
 *         On exit, its eigenvalues.  
 *  
 *  E      (input) DOUBLE PRECISION array, dimension (N-1)  
 *         The off-diagonal elements of the tridiagonal matrix.  
 *         On exit, E has been destroyed.  
 *  
 *  Q      (input/output) DOUBLE PRECISION array, dimension (LDQ, N)  
 *         On entry, Q must contain an N-by-N orthogonal matrix.  
 *         If ICOMPQ = 0    Q is not referenced.  
 *         If ICOMPQ = 1    On entry, Q is a subset of the columns of the  
 *                          orthogonal matrix used to reduce the full  
 *                          matrix to tridiagonal form corresponding to  
 *                          the subset of the full matrix which is being  
 *                          decomposed at this time.  
 *         If ICOMPQ = 2    On entry, Q will be the identity matrix.  
 *                          On exit, Q contains the eigenvectors of the  
 *                          tridiagonal matrix.  
 *  
 *  LDQ    (input) INTEGER  
 *         The leading dimension of the array Q.  If eigenvectors are  
 *         desired, then  LDQ >= max(1,N).  In any case,  LDQ >= 1.  
 *  
 *  QSTORE (workspace) DOUBLE PRECISION array, dimension (LDQS, N)  
 *         Referenced only when ICOMPQ = 1.  Used to store parts of  
 *         the eigenvector matrix when the updating matrix multiplies  
 *         take place.  
 *  
 *  LDQS   (input) INTEGER  
 *         The leading dimension of the array QSTORE.  If ICOMPQ = 1,  
 *         then  LDQS >= max(1,N).  In any case,  LDQS >= 1.  
 *  
 *  WORK   (workspace) DOUBLE PRECISION array,  
 *         If ICOMPQ = 0 or 1, the dimension of WORK must be at least  
 *                     1 + 3*N + 2*N*lg N + 2*N**2  
 *                     ( lg( N ) = smallest integer k  
 *                                 such that 2^k >= N )  
 *         If ICOMPQ = 2, the dimension of WORK must be at least  
 *                     4*N + N**2.  
 *  
 *  IWORK  (workspace) INTEGER array,  
 *         If ICOMPQ = 0 or 1, the dimension of IWORK must be at least  
 *                        6 + 6*N + 5*N*lg N.  
 *                        ( lg( N ) = smallest integer k  
 *                                    such that 2^k >= N )  
 *         If ICOMPQ = 2, the dimension of IWORK must be at least  
 *                        3 + 5*N.  
 *  
 *  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  
 *  
 *  =====================================================================  *  =====================================================================
 *  *
 *     .. Parameters ..  *     .. Parameters ..
Removed from v.1.2  
changed lines
  Added in v.1.18

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