dlaeda.f

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*> \brief \b DLAEDA used by DSTEDC. Computes the Z vector determining the rank-one modification of the diagonal matrix. Used when the original matrix is dense.
*
*  =========== DOCUMENTATION ===========
*
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*            http://www.netlib.org/lapack/explore-html/
*
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*
*  Definition:
*  ===========
*
*       SUBROUTINE DLAEDA( N, TLVLS, CURLVL, CURPBM, PRMPTR, PERM, GIVPTR,
*                          GIVCOL, GIVNUM, Q, QPTR, Z, ZTEMP, INFO )
*
*       .. Scalar Arguments ..
*       INTEGER            CURLVL, CURPBM, INFO, N, TLVLS
*       ..
*       .. Array Arguments ..
*       INTEGER            GIVCOL( 2, * ), GIVPTR( * ), PERM( * ),
*      $                   PRMPTR( * ), QPTR( * )
*       DOUBLE PRECISION   GIVNUM( 2, * ), Q( * ), Z( * ), ZTEMP( * )
*       ..
*
*
*> \par Purpose:
*  =============
*>
*> \verbatim
*>
*> DLAEDA computes the Z vector corresponding to the merge step in the
*> CURLVLth step of the merge process with TLVLS steps for the CURPBMth
*> problem.
*> \endverbatim
*
*  Arguments:
*  ==========
*
*> \param[in] N
*> \verbatim
*>          N is INTEGER
*>         The dimension of the symmetric tridiagonal matrix.  N >= 0.
*> \endverbatim
*>
*> \param[in] TLVLS
*> \verbatim
*>          TLVLS is INTEGER
*>         The total number of merging levels in the overall divide and
*>         conquer tree.
*> \endverbatim
*>
*> \param[in] CURLVL
*> \verbatim
*>          CURLVL is INTEGER
*>         The current level in the overall merge routine,
*>         0 <= curlvl <= tlvls.
*> \endverbatim
*>
*> \param[in] CURPBM
*> \verbatim
*>          CURPBM is INTEGER
*>         The current problem in the current level in the overall
*>         merge routine (counting from upper left to lower right).
*> \endverbatim
*>
*> \param[in] PRMPTR
*> \verbatim
*>          PRMPTR is INTEGER array, dimension (N lg N)
*>         Contains a list of pointers which indicate where in PERM a
*>         level's permutation is stored.  PRMPTR(i+1) - PRMPTR(i)
*>         indicates the size of the permutation and incidentally the
*>         size of the full, non-deflated problem.
*> \endverbatim
*>
*> \param[in] PERM
*> \verbatim
*>          PERM is INTEGER array, dimension (N lg N)
*>         Contains the permutations (from deflation and sorting) to be
*>         applied to each eigenblock.
*> \endverbatim
*>
*> \param[in] GIVPTR
*> \verbatim
*>          GIVPTR is INTEGER array, dimension (N lg N)
*>         Contains a list of pointers which indicate where in GIVCOL a
*>         level's Givens rotations are stored.  GIVPTR(i+1) - GIVPTR(i)
*>         indicates the number of Givens rotations.
*> \endverbatim
*>
*> \param[in] GIVCOL
*> \verbatim
*>          GIVCOL is INTEGER array, dimension (2, N lg N)
*>         Each pair of numbers indicates a pair of columns to take place
*>         in a Givens rotation.
*> \endverbatim
*>
*> \param[in] GIVNUM
*> \verbatim
*>          GIVNUM is DOUBLE PRECISION array, dimension (2, N lg N)
*>         Each number indicates the S value to be used in the
*>         corresponding Givens rotation.
*> \endverbatim
*>
*> \param[in] Q
*> \verbatim
*>          Q is DOUBLE PRECISION array, dimension (N**2)
*>         Contains the square eigenblocks from previous levels, the
*>         starting positions for blocks are given by QPTR.
*> \endverbatim
*>
*> \param[in] QPTR
*> \verbatim
*>          QPTR is INTEGER array, dimension (N+2)
*>         Contains a list of pointers which indicate where in Q an
*>         eigenblock is stored.  SQRT( QPTR(i+1) - QPTR(i) ) indicates
*>         the size of the block.
*> \endverbatim
*>
*> \param[out] Z
*> \verbatim
*>          Z is DOUBLE PRECISION array, dimension (N)
*>         On output this vector contains the updating vector (the last
*>         row of the first sub-eigenvector matrix and the first row of
*>         the second sub-eigenvector matrix).
*> \endverbatim
*>
*> \param[out] ZTEMP
*> \verbatim
*>          ZTEMP is DOUBLE PRECISION array, dimension (N)
*> \endverbatim
*>
*> \param[out] INFO
*> \verbatim
*>          INFO is INTEGER
*>          = 0:  successful exit.
*>          < 0:  if INFO = -i, the i-th argument had an illegal value.
*> \endverbatim
*
*  Authors:
*  ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \ingroup laeda
*
*> \par Contributors:
*  ==================
*>
*> Jeff Rutter, Computer Science Division, University of California
*> at Berkeley, USA
*
*  =====================================================================
      SUBROUTINE dlaeda( N, TLVLS, CURLVL, CURPBM, PRMPTR, PERM,
     $                   GIVPTR,
     $                   GIVCOL, GIVNUM, Q, QPTR, Z, ZTEMP, INFO )
*
*  -- LAPACK computational 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            CURLVL, CURPBM, INFO, N, TLVLS
*     ..
*     .. Array Arguments ..
      INTEGER            GIVCOL( 2, * ), GIVPTR( * ), PERM( * ),
     $                   PRMPTR( * ), QPTR( * )
      DOUBLE PRECISION   GIVNUM( 2, * ), Q( * ), Z( * ), ZTEMP( * )
*     ..
*
*  =====================================================================
*
*     .. Parameters ..
      DOUBLE PRECISION   ZERO, HALF, ONE
      PARAMETER          ( ZERO = 0.0d0, half = 0.5d0, one = 1.0d0 )
*     ..
*     .. Local Scalars ..
      INTEGER            BSIZ1, BSIZ2, CURR, I, K, MID, PSIZ1, PSIZ2,
     $                   PTR, ZPTR1
*     ..
*     .. External Subroutines ..
      EXTERNAL           dcopy, dgemv, drot, xerbla
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          dble, int, sqrt
*     ..
*     .. Executable Statements ..
*
*     Test the input parameters.
*
      info = 0
*
      IF( n.LT.0 ) THEN
         info = -1
      END IF
      IF( info.NE.0 ) THEN
         CALL xerbla( 'DLAEDA', -info )
         RETURN
      END IF
*
*     Quick return if possible
*
      IF( n.EQ.0 )
     $   RETURN
*
*     Determine location of first number in second half.
*
      mid = n / 2 + 1
*
*     Gather last/first rows of appropriate eigenblocks into center of Z
*
      ptr = 1
*
*     Determine location of lowest level subproblem in the full storage
*     scheme
*
      curr = ptr + curpbm*2**curlvl + 2**( curlvl-1 ) - 1
*
*     Determine size of these matrices.  We add HALF to the value of
*     the SQRT in case the machine underestimates one of these square
*     roots.
*
      bsiz1 = int( half+sqrt( dble( qptr( curr+1 )-qptr( curr ) ) ) )
      bsiz2 = int( half+sqrt( dble( qptr( curr+2 )-qptr( curr+1 ) ) ) )
      DO 10 k = 1, mid - bsiz1 - 1
         z( k ) = zero
   10 CONTINUE
      CALL dcopy( bsiz1, q( qptr( curr )+bsiz1-1 ), bsiz1,
     $            z( mid-bsiz1 ), 1 )
      CALL dcopy( bsiz2, q( qptr( curr+1 ) ), bsiz2, z( mid ), 1 )
      DO 20 k = mid + bsiz2, n
         z( k ) = zero
   20 CONTINUE
*
*     Loop through remaining levels 1 -> CURLVL applying the Givens
*     rotations and permutation and then multiplying the center matrices
*     against the current Z.
*
      ptr = 2**tlvls + 1
      DO 70 k = 1, curlvl - 1
         curr = ptr + curpbm*2**( curlvl-k ) + 2**( curlvl-k-1 ) - 1
         psiz1 = prmptr( curr+1 ) - prmptr( curr )
         psiz2 = prmptr( curr+2 ) - prmptr( curr+1 )
         zptr1 = mid - psiz1
*
*       Apply Givens at CURR and CURR+1
*
         DO 30 i = givptr( curr ), givptr( curr+1 ) - 1
            CALL drot( 1, z( zptr1+givcol( 1, i )-1 ), 1,
     $                 z( zptr1+givcol( 2, i )-1 ), 1, givnum( 1, i ),
     $                 givnum( 2, i ) )
   30    CONTINUE
         DO 40 i = givptr( curr+1 ), givptr( curr+2 ) - 1
            CALL drot( 1, z( mid-1+givcol( 1, i ) ), 1,
     $                 z( mid-1+givcol( 2, i ) ), 1, givnum( 1, i ),
     $                 givnum( 2, i ) )
   40    CONTINUE
         psiz1 = prmptr( curr+1 ) - prmptr( curr )
         psiz2 = prmptr( curr+2 ) - prmptr( curr+1 )
         DO 50 i = 0, psiz1 - 1
            ztemp( i+1 ) = z( zptr1+perm( prmptr( curr )+i )-1 )
   50    CONTINUE
         DO 60 i = 0, psiz2 - 1
            ztemp( psiz1+i+1 ) = z( mid+perm( prmptr( curr+1 )+i )-1 )
   60    CONTINUE
*
*        Multiply Blocks at CURR and CURR+1
*
*        Determine size of these matrices.  We add HALF to the value of
*        the SQRT in case the machine underestimates one of these
*        square roots.
*
         bsiz1 = int( half+sqrt( dble( qptr( curr+1 )-qptr( curr ) ) ) )
         bsiz2 = int( half+sqrt( dble( qptr( curr+2 )-qptr( curr+
     $           1 ) ) ) )
         IF( bsiz1.GT.0 ) THEN
            CALL dgemv( 'T', bsiz1, bsiz1, one, q( qptr( curr ) ),
     $                  bsiz1, ztemp( 1 ), 1, zero, z( zptr1 ), 1 )
         END IF
         CALL dcopy( psiz1-bsiz1, ztemp( bsiz1+1 ), 1,
     $               z( zptr1+bsiz1 ),
     $               1 )
         IF( bsiz2.GT.0 ) THEN
            CALL dgemv( 'T', bsiz2, bsiz2, one, q( qptr( curr+1 ) ),
     $                  bsiz2, ztemp( psiz1+1 ), 1, zero, z( mid ), 1 )
         END IF
         CALL dcopy( psiz2-bsiz2, ztemp( psiz1+bsiz2+1 ), 1,
     $               z( mid+bsiz2 ), 1 )
*
         ptr = ptr + 2**( tlvls-k )
   70 CONTINUE
*
      RETURN
*
*     End of DLAEDA
*
      END