# slaed4.f(3) [centos man page]

```slaed4.f(3)							      LAPACK							       slaed4.f(3)

NAME
slaed4.f -

SYNOPSIS
Functions/Subroutines
subroutine slaed4 (N, I, D, Z, DELTA, RHO, DLAM, INFO)
SLAED4 used by sstedc. Finds a single root of the secular equation.

Function/Subroutine Documentation
subroutine slaed4 (integerN, integerI, real, dimension( * )D, real, dimension( * )Z, real, dimension( * )DELTA, realRHO, realDLAM, integerINFO)
SLAED4 used by sstedc. Finds a single root of the secular equation.

Purpose:

This subroutine computes the I-th updated eigenvalue of a symmetric
rank-one modification to a diagonal matrix whose elements are
given in the array d, and that

D(i) < D(j)  for  i < j

and that RHO > 0.  This is arranged by the calling routine, and is
no loss in generality.  The rank-one modified system is thus

diag( D )  +  RHO * Z * Z_transpose.

where we assume the Euclidean norm of Z is 1.

The method consists of approximating the rational functions in the
secular equation by simpler interpolating rational functions.

Parameters:
N

N is INTEGER
The length of all arrays.

I

I is INTEGER
The index of the eigenvalue to be computed.  1 <= I <= N.

D

D is REAL array, dimension (N)
The original eigenvalues.  It is assumed that they are in
order, D(I) < D(J)	for I < J.

Z

Z is REAL array, dimension (N)
The components of the updating vector.

DELTA

DELTA is REAL array, dimension (N)
If N .GT. 2, DELTA contains (D(j) - lambda_I) in its  j-th
component.	If N = 1, then DELTA(1) = 1. If N = 2, see SLAED5
for detail. The vector DELTA contains the information necessary
to construct the eigenvectors by SLAED3 and SLAED9.

RHO

RHO is REAL
The scalar in the symmetric updating formula.

DLAM

DLAM is REAL
The computed lambda_I, the I-th updated eigenvalue.

INFO

INFO is INTEGER
= 0:  successful exit
> 0:  if INFO = 1, the updating process failed.

Internal Parameters:

Logical variable ORGATI (origin-at-i?) is used for distinguishing
whether D(i) or D(i+1) is treated as the origin.

ORGATI = .true.	  origin at i
ORGATI = .false.   origin at i+1

Logical variable SWTCH3 (switch-for-3-poles?) is for noting
if we are working with THREE poles!

MAXIT is the maximum number of iterations allowed for each
eigenvalue.

Author:
Univ. of Tennessee

Univ. of California Berkeley

NAG Ltd.

Date:
September 2012

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

Definition at line 146 of file slaed4.f.

Author
Generated automatically by Doxygen for LAPACK from the source code.

Version 3.4.2							  Tue Sep 25 2012						       slaed4.f(3)```

## Check Out this Related Man Page

```SLAED4(l)								 )								 SLAED4(l)

NAME
SLAED4 - subroutine computes the I-th updated eigenvalue of a symmetric rank-one modification to a diagonal matrix whose elements are given
in the array d, and that  D(i) < D(j) for i < j	and that RHO > 0

SYNOPSIS
SUBROUTINE SLAED4( N, I, D, Z, DELTA, RHO, DLAM, INFO )

INTEGER	  I, INFO, N

REAL 	  DLAM, RHO

REAL 	  D( * ), DELTA( * ), Z( * )

PURPOSE
This subroutine computes the I-th updated eigenvalue of a symmetric rank-one modification to a diagonal matrix whose elements are given	in
the  array  d, and that D(i) < D(j) for i < j and that RHO > 0. This is arranged by the calling routine, and is no loss in generality.  The
rank-one modified system is thus

diag( D )  +	RHO *  Z * Z_transpose.

where we assume the Euclidean norm of Z is 1.

The method consists of approximating the rational functions in the secular equation by simpler interpolating rational functions.

ARGUMENTS
N      (input) INTEGER
The length of all arrays.

I      (input) INTEGER
The index of the eigenvalue to be computed.  1 <= I <= N.

D      (input) REAL array, dimension (N)
The original eigenvalues.  It is assumed that they are in order, D(I) < D(J)  for I < J.

Z      (input) REAL array, dimension (N)
The components of the updating vector.

DELTA  (output) REAL array, dimension (N)
If N .ne. 1, DELTA contains (D(j) - lambda_I) in its  j-th component.  If N = 1, then DELTA(1) = 1.  The vector DELTA  contains  the
information necessary to construct the eigenvectors.

RHO    (input) REAL
The scalar in the symmetric updating formula.

DLAM   (output) REAL
The computed lambda_I, the I-th updated eigenvalue.

INFO   (output) INTEGER
= 0:  successful exit
> 0:  if INFO = 1, the updating process failed.

PARAMETERS
Logical variable ORGATI (origin-at-i?) is used for distinguishing whether D(i) or D(i+1) is treated as the origin.

ORGATI = .true.	  origin at i ORGATI = .false.	 origin at i+1

Logical variable SWTCH3 (switch-for-3-poles?) is for noting if we are working with THREE poles!

MAXIT is the maximum number of iterations allowed for each eigenvalue.

Further Details ===============

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

LAPACK version 3.0						   15 June 2000 							 SLAED4(l)```
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