laed6(3)

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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