NAME

       slaed9.f -

SYNOPSIS

   Functions/Subroutines
       subroutine slaed9 (K, KSTART, KSTOP, N, D, Q, LDQ, RHO, DLAMDA, W, S, LDS, INFO)
           SLAED9 used by sstedc. Finds the roots of the secular equation and updates the
           eigenvectors. Used when the original matrix is dense.

Function/Subroutine Documentation

   subroutine slaed9 (integer K, integer KSTART, integer KSTOP, integer N, real, dimension( * )
       D, real, dimension( ldq, * ) Q, integer LDQ, real RHO, real, dimension( * ) DLAMDA, real,
       dimension( * ) W, real, dimension( lds, * ) S, integer LDS, integer INFO)
       SLAED9 used by sstedc. Finds the roots of the secular equation and updates the
       eigenvectors. Used when the original matrix is dense.

       Purpose:

            SLAED9 finds the roots of the secular equation, as defined by the
            values in D, Z, and RHO, between KSTART and KSTOP.  It makes the
            appropriate calls to SLAED4 and then stores the new matrix of
            eigenvectors for use in calculating the next level of Z vectors.

       Parameters:
           K

                     K is INTEGER
                     The number of terms in the rational function to be solved by
                     SLAED4.  K >= 0.

           KSTART

                     KSTART is INTEGER

           KSTOP

                     KSTOP is INTEGER
                     The updated eigenvalues Lambda(I), KSTART <= I <= KSTOP
                     are to be computed.  1 <= KSTART <= KSTOP <= K.

           N

                     N is INTEGER
                     The number of rows and columns in the Q matrix.
                     N >= K (delation may result in N > K).

           D

                     D is REAL array, dimension (N)
                     D(I) contains the updated eigenvalues
                     for KSTART <= I <= KSTOP.

           Q

                     Q is REAL array, dimension (LDQ,N)

           LDQ

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

           RHO

                     RHO is REAL
                     The value of the parameter in the rank one update equation.
                     RHO >= 0 required.

           DLAMDA

                     DLAMDA is REAL array, dimension (K)
                     The first K elements of this array contain the old roots
                     of the deflated updating problem.  These are the poles
                     of the secular equation.

           W

                     W is REAL array, dimension (K)
                     The first K elements of this array contain the components
                     of the deflation-adjusted updating vector.

           S

                     S is REAL array, dimension (LDS, K)
                     Will contain the eigenvectors of the repaired matrix which
                     will be stored for subsequent Z vector calculation and
                     multiplied by the previously accumulated eigenvectors
                     to update the system.

           LDS

                     LDS is INTEGER
                     The leading dimension of S.  LDS >= max( 1, K ).

           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

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

Author

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