# laed6 - Man Page

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.

## 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

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

Definition at line 139 of file dlaed6.f.

### 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

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

Definition at line 139 of file slaed6.f.

## Author

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## Info

Tue Nov 28 2023 12:08:43 Version 3.12.0 LAPACK