slasdt.f

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*> \brief \b SLASDT creates a tree of subproblems for bidiagonal divide and conquer. Used by sbdsdc.
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at
*            http://www.netlib.org/lapack/explore-html/
*
*> \htmlonly
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*> \endhtmlonly
*
*  Definition:
*  ===========
*
*       SUBROUTINE SLASDT( N, LVL, ND, INODE, NDIML, NDIMR, MSUB )
*
*       .. Scalar Arguments ..
*       INTEGER            LVL, MSUB, N, ND
*       ..
*       .. Array Arguments ..
*       INTEGER            INODE( * ), NDIML( * ), NDIMR( * )
*       ..
*
*
*> \par Purpose:
*  =============
*>
*> \verbatim
*>
*> SLASDT creates a tree of subproblems for bidiagonal divide and
*> conquer.
*> \endverbatim
*
*  Arguments:
*  ==========
*
*> \param[in] N
*> \verbatim
*>          N is INTEGER
*>          On entry, the number of diagonal elements of the
*>          bidiagonal matrix.
*> \endverbatim
*>
*> \param[out] LVL
*> \verbatim
*>          LVL is INTEGER
*>          On exit, the number of levels on the computation tree.
*> \endverbatim
*>
*> \param[out] ND
*> \verbatim
*>          ND is INTEGER
*>          On exit, the number of nodes on the tree.
*> \endverbatim
*>
*> \param[out] INODE
*> \verbatim
*>          INODE is INTEGER array, dimension ( N )
*>          On exit, centers of subproblems.
*> \endverbatim
*>
*> \param[out] NDIML
*> \verbatim
*>          NDIML is INTEGER array, dimension ( N )
*>          On exit, row dimensions of left children.
*> \endverbatim
*>
*> \param[out] NDIMR
*> \verbatim
*>          NDIMR is INTEGER array, dimension ( N )
*>          On exit, row dimensions of right children.
*> \endverbatim
*>
*> \param[in] MSUB
*> \verbatim
*>          MSUB is INTEGER
*>          On entry, the maximum row dimension each subproblem at the
*>          bottom of the tree can be of.
*> \endverbatim
*
*  Authors:
*  ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \ingroup lasdt
*
*> \par Contributors:
*  ==================
*>
*>     Ming Gu and Huan Ren, Computer Science Division, University of
*>     California at Berkeley, USA
*>
*  =====================================================================
      SUBROUTINE slasdt( N, LVL, ND, INODE, NDIML, NDIMR, MSUB )
*
*  -- LAPACK auxiliary routine --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*
*     .. Scalar Arguments ..
      INTEGER            LVL, MSUB, N, ND
*     ..
*     .. Array Arguments ..
      INTEGER            INODE( * ), NDIML( * ), NDIMR( * )
*     ..
*
*  =====================================================================
*
*     .. Parameters ..
      REAL               TWO
      parameter( two = 2.0e+0 )
*     ..
*     .. Local Scalars ..
      INTEGER            I, IL, IR, LLST, MAXN, NCRNT, NLVL
      REAL               TEMP
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          int, log, max, real
*     ..
*     .. Executable Statements ..
*
*     Find the number of levels on the tree.
*
      maxn = max( 1, n )
      temp = log( real( maxn ) / real( msub+1 ) ) / log( two )
      lvl = int( temp ) + 1
*
      i = n / 2
      inode( 1 ) = i + 1
      ndiml( 1 ) = i
      ndimr( 1 ) = n - i - 1
      il = 0
      ir = 1
      llst = 1
      DO 20 nlvl = 1, lvl - 1
*
*        Constructing the tree at (NLVL+1)-st level. The number of
*        nodes created on this level is LLST * 2.
*
         DO 10 i = 0, llst - 1
            il = il + 2
            ir = ir + 2
            ncrnt = llst + i
            ndiml( il ) = ndiml( ncrnt ) / 2
            ndimr( il ) = ndiml( ncrnt ) - ndiml( il ) - 1
            inode( il ) = inode( ncrnt ) - ndimr( il ) - 1
            ndiml( ir ) = ndimr( ncrnt ) / 2
            ndimr( ir ) = ndimr( ncrnt ) - ndiml( ir ) - 1
            inode( ir ) = inode( ncrnt ) + ndiml( ir ) + 1
   10    CONTINUE
         llst = llst*2
   20 CONTINUE
      nd = llst*2 - 1
*
      RETURN
*
*     End of SLASDT
*
      END