slaed9(3S)

NAME
     SLAED9 - 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( * )

IMPLEMENTATION
     These routines are part of the SCSL Scientific Library and can be loaded
     using either the -lscs or the -lscs_mp option.  The -lscs_mp option
     directs the linker to use the multi-processor version of the library.

     When linking to SCSL with -lscs or -lscs_mp, the default integer size is
     4 bytes (32 bits). Another version of SCSL is available in which integers
     are 8 bytes (64 bits).  This version allows the user access to larger
     memory sizes and helps when porting legacy Cray codes.  It can be loaded
     by using the -lscs_i8 option or the -lscs_i8_mp option. A program may use
     only one of the two versions; 4-byte integer and 8-byte integer library
     calls cannot be mixed.

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

FURTHER DETAILS
     Based on contributions by
        Jeff Rutter, Computer Science Division, University of California
        at Berkeley, USA


SEE ALSO
     INTRO_LAPACK(3S), INTRO_SCSL(3S)

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