NAME

       dlaeda.f -

SYNOPSIS

   Functions/Subroutines
       subroutine dlaeda (N, TLVLS, CURLVL, CURPBM, PRMPTR, PERM, GIVPTR, GIVCOL, GIVNUM, Q,
           QPTR, Z, ZTEMP, INFO)
           DLAEDA used by sstedc. Computes the Z vector determining the rank-one modification of
           the diagonal matrix. Used when the original matrix is dense.

Function/Subroutine Documentation

   subroutine dlaeda (integer N, integer TLVLS, integer CURLVL, integer CURPBM, integer,
       dimension( * ) PRMPTR, integer, dimension( * ) PERM, integer, dimension( * ) GIVPTR,
       integer, dimension( 2, * ) GIVCOL, double precision, dimension( 2, * ) GIVNUM, double
       precision, dimension( * ) Q, integer, dimension( * ) QPTR, double precision, dimension( *
       ) Z, double precision, dimension( * ) ZTEMP, integer INFO)
       DLAEDA used by sstedc. Computes the Z vector determining the rank-one modification of the
       diagonal matrix. Used when the original matrix is dense.

       Purpose:

            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.

       Parameters:
           N

                     N is INTEGER
                    The dimension of the symmetric tridiagonal matrix.  N >= 0.

           TLVLS

                     TLVLS is INTEGER
                    The total number of merging levels in the overall divide and
                    conquer tree.

           CURLVL

                     CURLVL is INTEGER
                    The current level in the overall merge routine,
                    0 <= curlvl <= tlvls.

           CURPBM

                     CURPBM is INTEGER
                    The current problem in the current level in the overall
                    merge routine (counting from upper left to lower right).

           PRMPTR

                     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.

           PERM

                     PERM is INTEGER array, dimension (N lg N)
                    Contains the permutations (from deflation and sorting) to be
                    applied to each eigenblock.

           GIVPTR

                     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.

           GIVCOL

                     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.

           GIVNUM

                     GIVNUM is DOUBLE PRECISION array, dimension (2, N lg N)
                    Each number indicates the S value to be used in the
                    corresponding Givens rotation.

           Q

                     Q is DOUBLE PRECISION array, dimension (N**2)
                    Contains the square eigenblocks from previous levels, the
                    starting positions for blocks are given by QPTR.

           QPTR

                     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.

           Z

                     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).

           ZTEMP

                     ZTEMP is DOUBLE PRECISION array, dimension (N)

           INFO

                     INFO is INTEGER
                     = 0:  successful exit.
                     < 0:  if INFO = -i, the i-th argument had an illegal value.

       Author:
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

       Date:
           September 2012

       Contributors:
           Jeff Rutter, Computer Science Division, University of California at Berkeley, USA

Author

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