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version 1.9, 2011/07/22 07:38:07 version 1.10, 2011/11/21 20:42:58
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   *> \brief \b DLASD0
   *
   *  =========== DOCUMENTATION ===========
   *
   * Online html documentation available at 
   *            http://www.netlib.org/lapack/explore-html/ 
   *
   *> \htmlonly
   *> Download DLASD0 + dependencies 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlasd0.f"> 
   *> [TGZ]</a> 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlasd0.f"> 
   *> [ZIP]</a> 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlasd0.f"> 
   *> [TXT]</a>
   *> \endhtmlonly 
   *
   *  Definition:
   *  ===========
   *
   *       SUBROUTINE DLASD0( N, SQRE, D, E, U, LDU, VT, LDVT, SMLSIZ, IWORK,
   *                          WORK, INFO )
   * 
   *       .. Scalar Arguments ..
   *       INTEGER            INFO, LDU, LDVT, N, SMLSIZ, SQRE
   *       ..
   *       .. Array Arguments ..
   *       INTEGER            IWORK( * )
   *       DOUBLE PRECISION   D( * ), E( * ), U( LDU, * ), VT( LDVT, * ),
   *      $                   WORK( * )
   *       ..
   *  
   *
   *> \par Purpose:
   *  =============
   *>
   *> \verbatim
   *>
   *> Using a divide and conquer approach, DLASD0 computes the singular
   *> value decomposition (SVD) of a real upper bidiagonal N-by-M
   *> matrix B with diagonal D and offdiagonal E, where M = N + SQRE.
   *> The algorithm computes orthogonal matrices U and VT such that
   *> B = U * S * VT. The singular values S are overwritten on D.
   *>
   *> A related subroutine, DLASDA, computes only the singular values,
   *> and optionally, the singular vectors in compact form.
   *> \endverbatim
   *
   *  Arguments:
   *  ==========
   *
   *> \param[in] N
   *> \verbatim
   *>          N is INTEGER
   *>         On entry, the row dimension of the upper bidiagonal matrix.
   *>         This is also the dimension of the main diagonal array D.
   *> \endverbatim
   *>
   *> \param[in] SQRE
   *> \verbatim
   *>          SQRE is INTEGER
   *>         Specifies the column dimension of the bidiagonal matrix.
   *>         = 0: The bidiagonal matrix has column dimension M = N;
   *>         = 1: The bidiagonal matrix has column dimension M = N+1;
   *> \endverbatim
   *>
   *> \param[in,out] D
   *> \verbatim
   *>          D is DOUBLE PRECISION array, dimension (N)
   *>         On entry D contains the main diagonal of the bidiagonal
   *>         matrix.
   *>         On exit D, if INFO = 0, contains its singular values.
   *> \endverbatim
   *>
   *> \param[in] E
   *> \verbatim
   *>          E is DOUBLE PRECISION array, dimension (M-1)
   *>         Contains the subdiagonal entries of the bidiagonal matrix.
   *>         On exit, E has been destroyed.
   *> \endverbatim
   *>
   *> \param[out] U
   *> \verbatim
   *>          U is DOUBLE PRECISION array, dimension at least (LDQ, N)
   *>         On exit, U contains the left singular vectors.
   *> \endverbatim
   *>
   *> \param[in] LDU
   *> \verbatim
   *>          LDU is INTEGER
   *>         On entry, leading dimension of U.
   *> \endverbatim
   *>
   *> \param[out] VT
   *> \verbatim
   *>          VT is DOUBLE PRECISION array, dimension at least (LDVT, M)
   *>         On exit, VT**T contains the right singular vectors.
   *> \endverbatim
   *>
   *> \param[in] LDVT
   *> \verbatim
   *>          LDVT is INTEGER
   *>         On entry, leading dimension of VT.
   *> \endverbatim
   *>
   *> \param[in] SMLSIZ
   *> \verbatim
   *>          SMLSIZ is INTEGER
   *>         On entry, maximum size of the subproblems at the
   *>         bottom of the computation tree.
   *> \endverbatim
   *>
   *> \param[out] IWORK
   *> \verbatim
   *>          IWORK is INTEGER work array.
   *>         Dimension must be at least (8 * N)
   *> \endverbatim
   *>
   *> \param[out] WORK
   *> \verbatim
   *>          WORK is DOUBLE PRECISION work array.
   *>         Dimension must be at least (3 * M**2 + 2 * M)
   *> \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 = 1, a singular value did not converge
   *> \endverbatim
   *
   *  Authors:
   *  ========
   *
   *> \author Univ. of Tennessee 
   *> \author Univ. of California Berkeley 
   *> \author Univ. of Colorado Denver 
   *> \author NAG Ltd. 
   *
   *> \date November 2011
   *
   *> \ingroup auxOTHERauxiliary
   *
   *> \par Contributors:
   *  ==================
   *>
   *>     Ming Gu and Huan Ren, Computer Science Division, University of
   *>     California at Berkeley, USA
   *>
   *  =====================================================================
       SUBROUTINE DLASD0( N, SQRE, D, E, U, LDU, VT, LDVT, SMLSIZ, IWORK,        SUBROUTINE DLASD0( N, SQRE, D, E, U, LDU, VT, LDVT, SMLSIZ, IWORK,
      $                   WORK, INFO )       $                   WORK, INFO )
 *  *
 *  -- LAPACK auxiliary routine (version 3.2.2) --  *  -- LAPACK auxiliary 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..--
 *     June 2010  *     November 2011
 *  *
 *     .. Scalar Arguments ..  *     .. Scalar Arguments ..
       INTEGER            INFO, LDU, LDVT, N, SMLSIZ, SQRE        INTEGER            INFO, LDU, LDVT, N, SMLSIZ, SQRE
Line 15 Line 166
      $                   WORK( * )       $                   WORK( * )
 *     ..  *     ..
 *  *
 *  Purpose  
 *  =======  
 *  
 *  Using a divide and conquer approach, DLASD0 computes the singular  
 *  value decomposition (SVD) of a real upper bidiagonal N-by-M  
 *  matrix B with diagonal D and offdiagonal E, where M = N + SQRE.  
 *  The algorithm computes orthogonal matrices U and VT such that  
 *  B = U * S * VT. The singular values S are overwritten on D.  
 *  
 *  A related subroutine, DLASDA, computes only the singular values,  
 *  and optionally, the singular vectors in compact form.  
 *  
 *  Arguments  
 *  =========  
 *  
 *  N      (input) INTEGER  
 *         On entry, the row dimension of the upper bidiagonal matrix.  
 *         This is also the dimension of the main diagonal array D.  
 *  
 *  SQRE   (input) INTEGER  
 *         Specifies the column dimension of the bidiagonal matrix.  
 *         = 0: The bidiagonal matrix has column dimension M = N;  
 *         = 1: The bidiagonal matrix has column dimension M = N+1;  
 *  
 *  D      (input/output) DOUBLE PRECISION array, dimension (N)  
 *         On entry D contains the main diagonal of the bidiagonal  
 *         matrix.  
 *         On exit D, if INFO = 0, contains its singular values.  
 *  
 *  E      (input) DOUBLE PRECISION array, dimension (M-1)  
 *         Contains the subdiagonal entries of the bidiagonal matrix.  
 *         On exit, E has been destroyed.  
 *  
 *  U      (output) DOUBLE PRECISION array, dimension at least (LDQ, N)  
 *         On exit, U contains the left singular vectors.  
 *  
 *  LDU    (input) INTEGER  
 *         On entry, leading dimension of U.  
 *  
 *  VT     (output) DOUBLE PRECISION array, dimension at least (LDVT, M)  
 *         On exit, VT**T contains the right singular vectors.  
 *  
 *  LDVT   (input) INTEGER  
 *         On entry, leading dimension of VT.  
 *  
 *  SMLSIZ (input) INTEGER  
 *         On entry, maximum size of the subproblems at the  
 *         bottom of the computation tree.  
 *  
 *  IWORK  (workspace) INTEGER work array.  
 *         Dimension must be at least (8 * N)  
 *  
 *  WORK   (workspace) DOUBLE PRECISION work array.  
 *         Dimension must be at least (3 * M**2 + 2 * M)  
 *  
 *  INFO   (output) INTEGER  
 *          = 0:  successful exit.  
 *          < 0:  if INFO = -i, the i-th argument had an illegal value.  
 *          > 0:  if INFO = 1, a singular value did not converge  
 *  
 *  Further Details  
 *  ===============  
 *  
 *  Based on contributions by  
 *     Ming Gu and Huan Ren, Computer Science Division, University of  
 *     California at Berkeley, USA  
 *  
 *  =====================================================================  *  =====================================================================
 *  *
 *     .. Local Scalars ..  *     .. Local Scalars ..
Removed from v.1.9  
changed lines
  Added in v.1.10

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