NAME

       zlaed7.f -

SYNOPSIS

   Functions/Subroutines
       subroutine zlaed7 (N, CUTPNT, QSIZ, TLVLS, CURLVL, CURPBM, D, Q, LDQ, RHO, INDXQ, QSTORE,
           QPTR, PRMPTR, PERM, GIVPTR, GIVCOL, GIVNUM, WORK, RWORK, IWORK, INFO)
           ZLAED7 used by sstedc. Computes the updated eigensystem of a diagonal matrix after
           modification by a rank-one symmetric matrix. Used when the original matrix is dense.

Function/Subroutine Documentation

   subroutine zlaed7 (integer N, integer CUTPNT, integer QSIZ, integer TLVLS, integer CURLVL,
       integer CURPBM, double precision, dimension( * ) D, complex*16, dimension( ldq, * ) Q,
       integer LDQ, double precision RHO, integer, dimension( * ) INDXQ, double precision,
       dimension( * ) QSTORE, integer, dimension( * ) QPTR, integer, dimension( * ) PRMPTR,
       integer, dimension( * ) PERM, integer, dimension( * ) GIVPTR, integer, dimension( 2, * )
       GIVCOL, double precision, dimension( 2, * ) GIVNUM, complex*16, dimension( * ) WORK,
       double precision, dimension( * ) RWORK, integer, dimension( * ) IWORK, integer INFO)
       ZLAED7 used by sstedc. Computes the updated eigensystem of a diagonal matrix after
       modification by a rank-one symmetric matrix. Used when the original matrix is dense.

       Purpose:

            ZLAED7 computes the updated eigensystem of a diagonal
            matrix after modification by a rank-one symmetric matrix. This
            routine is used only for the eigenproblem which requires all
            eigenvalues and optionally eigenvectors of a dense or banded
            Hermitian matrix that has been reduced to tridiagonal form.

              T = Q(in) ( D(in) + RHO * Z*Z**H ) Q**H(in) = Q(out) * D(out) * Q**H(out)

              where Z = Q**Hu, u is a vector of length N with ones in the
              CUTPNT and CUTPNT + 1 th elements and zeros elsewhere.

               The eigenvectors of the original matrix are stored in Q, and the
               eigenvalues are in D.  The algorithm consists of three stages:

                  The first stage consists of deflating the size of the problem
                  when there are multiple eigenvalues or if there is a zero in
                  the Z vector.  For each such occurrence the dimension of the
                  secular equation problem is reduced by one.  This stage is
                  performed by the routine DLAED2.

                  The second stage consists of calculating the updated
                  eigenvalues. This is done by finding the roots of the secular
                  equation via the routine DLAED4 (as called by SLAED3).
                  This routine also calculates the eigenvectors of the current
                  problem.

                  The final stage consists of computing the updated eigenvectors
                  directly using the updated eigenvalues.  The eigenvectors for
                  the current problem are multiplied with the eigenvectors from
                  the overall problem.

       Parameters:
           N

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

           CUTPNT

                     CUTPNT is INTEGER
                    Contains the location of the last eigenvalue in the leading
                    sub-matrix.  min(1,N) <= CUTPNT <= N.

           QSIZ

                     QSIZ is INTEGER
                    The dimension of the unitary matrix used to reduce
                    the full matrix to tridiagonal form.  QSIZ >= N.

           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).

           D

                     D is DOUBLE PRECISION array, dimension (N)
                    On entry, the eigenvalues of the rank-1-perturbed matrix.
                    On exit, the eigenvalues of the repaired matrix.

           Q

                     Q is COMPLEX*16 array, dimension (LDQ,N)
                    On entry, the eigenvectors of the rank-1-perturbed matrix.
                    On exit, the eigenvectors of the repaired tridiagonal matrix.

           LDQ

                     LDQ is INTEGER
                    The leading dimension of the array Q.  LDQ >= max(1,N).

           RHO

                     RHO is DOUBLE PRECISION
                    Contains the subdiagonal element used to create the rank-1
                    modification.

           INDXQ

                     INDXQ is INTEGER array, dimension (N)
                    This contains the permutation which will reintegrate the
                    subproblem just solved back into sorted order,
                    ie. D( INDXQ( I = 1, N ) ) will be in ascending order.

           IWORK

                     IWORK is INTEGER array, dimension (4*N)

           RWORK

                     RWORK is DOUBLE PRECISION array,
                                            dimension (3*N+2*QSIZ*N)

           WORK

                     WORK is COMPLEX*16 array, dimension (QSIZ*N)

           QSTORE

                     QSTORE is DOUBLE PRECISION array, dimension (N**2+1)
                    Stores eigenvectors of submatrices encountered during
                    divide and conquer, packed together. QPTR points to
                    beginning of the submatrices.

           QPTR

                     QPTR is INTEGER array, dimension (N+2)
                    List of indices pointing to beginning of submatrices stored
                    in QSTORE. The submatrices are numbered starting at the
                    bottom left of the divide and conquer tree, from left to
                    right and bottom to top.

           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 also 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.

           INFO

                     INFO is INTEGER
                     = 0:  successful exit.
                     < 0:  if INFO = -i, the i-th argument had an illegal value.
                     > 0:  if INFO = 1, an eigenvalue did not converge

       Author:
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

       Date:
           September 2012

Author

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