SLAED9 (3lapack)

find the roots of the secular equation, as defined by the values in D, Z, and RHO, between KSTART and KSTOP

SYNOPSIS

  SUBROUTINE SLAED9( K, KSTART, KSTOP, N, D, Q, LDQ, RHO, DLAMDA, W, S, LDS,
                     INFO )

      INTEGER        INFO, K, KSTART, KSTOP, LDQ, LDS, N

      REAL           RHO

      REAL           D( * ), DLAMDA( * ), Q( LDQ, * ), S( LDS, * ), W( * )

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.

ARGUMENTS

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

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

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

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

  Q       (workspace) REAL array, dimension (LDQ,N)

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

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

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

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

  INFO    (output) 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