Man page - laed6(3)

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Manual

laed6

NAME
SYNOPSIS
Functions
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)
subroutine slaed6 (integer kniter, logical orgati, real rho, real,dimension( 3 ) d, real, dimension( 3 ) z, real finit, real tau, integerinfo)
Author

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, integerinfo)

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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