NAME

       laed6 - laed6: D&C step: secular equation Newton step

SYNOPSIS

   Functions
       subroutine dlaed6 (kniter, orgati, rho, d, z, finit, tau, info)
           DLAED6 used by DSTEDC. Computes one Newton step in solution of the secular equation.
       subroutine slaed6 (kniter, orgati, rho, d, z, finit, tau, info)
           SLAED6 used by SSTEDC. Computes one Newton step in solution of the secular equation.

Detailed Description

Function Documentation

   subroutine dlaed6 (integer kniter, logical orgati, double precision rho, double precision,
       dimension( 3 ) d, double precision, dimension( 3 ) z, double precision finit, double
       precision tau, integer info)
       DLAED6 used by DSTEDC. Computes one Newton step in solution of the secular equation.

       Purpose:

            DLAED6 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 DLAED4 when necessary. In most cases,
            the root sought is the smallest in magnitude, though it might not be
            in some extremely rare situations.

       Parameters
           KNITER

                     KNITER is INTEGER
                          Refer to DLAED4 for its significance.

           ORGATI

                     ORGATI is 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
                          DLAED4 for further details.

           RHO

                     RHO is DOUBLE PRECISION
                          Refer to the equation f(x) above.

           D

                     D is DOUBLE PRECISION array, dimension (3)
                          D satisfies d(1) < d(2) < d(3).

           Z

                     Z is DOUBLE PRECISION array, dimension (3)
                          Each of the elements in z must be positive.

           FINIT

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

           TAU

                     TAU is DOUBLE PRECISION
                          The root of the equation f(x).

           INFO

                     INFO is INTEGER
                          = 0: successful exit
                          > 0: if INFO = 1, failure to converge

       Author
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

       Further Details:

             10/02/03: This version has a few statements commented out for thread
             safety (machine parameters are computed on each entry). SJH.

             05/10/06: Modified from a new version of Ren-Cang Li, use
                Gragg-Thornton-Warner cubic convergent scheme for better stability.

       Contributors:
           Ren-Cang Li, Computer Science Division, University of California at Berkeley, USA

   subroutine slaed6 (integer kniter, logical orgati, real rho, real, dimension( 3 ) d, real,
       dimension( 3 ) z, real finit, real tau, integer info)
       SLAED6 used by SSTEDC. Computes one Newton step in solution of the secular equation.

       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.

       Parameters
           KNITER

                     KNITER is INTEGER
                          Refer to SLAED4 for its significance.

           ORGATI

                     ORGATI is 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

                     RHO is REAL
                          Refer to the equation f(x) above.

           D

                     D is REAL array, dimension (3)
                          D satisfies d(1) < d(2) < d(3).

           Z

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

           FINIT

                     FINIT is 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

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

           INFO

                     INFO is INTEGER
                          = 0: successful exit
                          > 0: if INFO = 1, failure to converge

       Author
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

       Further Details:

             10/02/03: This version has a few statements commented out for thread
             safety (machine parameters are computed on each entry). SJH.

             05/10/06: Modified from a new version of Ren-Cang Li, use
                Gragg-Thornton-Warner cubic convergent scheme for better stability.

       Contributors:
           Ren-Cang Li, Computer Science Division, University of California at Berkeley, USA

Author

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