slaed6(3S)

NAME
     SLAED6 - compute the positive or negative root (closest to the origin) of
     z(1) z(2) z(3) f(x) = rho + --------- + ---------- + --------- d(1)-x
     d(2)-x d(3)-x  It is assumed that  if ORGATI = .true

SYNOPSIS
     SUBROUTINE SLAED6( KNITER, ORGATI, RHO, D, Z, FINIT, TAU, INFO )

         LOGICAL        ORGATI

         INTEGER        INFO, KNITER

         REAL           FINIT, RHO, TAU

         REAL           D( 3 ), Z( 3 )

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
     SLAED6 computes the positive or negative root (closest to the origin) of
     z(1) z(2) z(3) f(x) = rho + --------- + ---------- + --------- d(1)-x
     d(2)-x d(3)-x It is assumed that if ORGATI = .true. the root is between
     d(2) and d(3);       otherwise it is between d(1) and d(2)

     This routine will be called by SLAED4 when necessary. In most cases, the
     root sought is the smallest in magnitude, though it might not be in some
     extremely rare situations.


ARGUMENTS
     KNITER       (input) INTEGER
                  Refer to SLAED4 for its significance.

     ORGATI       (input) LOGICAL
                  If ORGATI is true, the needed root is between d(2) and d(3);
                  otherwise it is between d(1) and d(2).  See SLAED4 for
                  further details.

     RHO          (input) REAL
                  Refer to the equation f(x) above.
     D            (input) REAL array, dimension (3)
                  D satisfies d(1) < d(2) < d(3).

     Z            (input) REAL array, dimension (3)
                  Each of the elements in z must be positive.

     FINIT        (input) REAL
                  The value of f at 0. It is more accurate than the one
                  evaluated inside this routine (if someone wants to do so).

     TAU          (output) REAL
                  The root of the equation f(x).

     INFO         (output) INTEGER
                  = 0: successful exit
                  > 0: if INFO = 1, failure to converge

FURTHER DETAILS
     Based on contributions by
        Ren-Cang Li, Computer Science Division, University of California
        at Berkeley, USA


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

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