# slasd4.f(3) [debian man page]

```slasd4.f(3)							      LAPACK							       slasd4.f(3)

NAME
slasd4.f -

SYNOPSIS
Functions/Subroutines
subroutine slasd4 (N, I, D, Z, DELTA, RHO, SIGMA, WORK, INFO)
SLASD4

Function/Subroutine Documentation
subroutine slasd4 (integerN, integerI, real, dimension( * )D, real, dimension( * )Z, real, dimension( * )DELTA, realRHO, realSIGMA, real,
dimension( * )WORK, integerINFO)
SLASD4

Purpose:

This subroutine computes the square root of the I-th updated
eigenvalue of a positive symmetric rank-one modification to
a positive diagonal matrix whose entries are given as the squares
of the corresponding entries in the array d, and that

0 <= 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 ) * 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, 0 <= 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 .ne. 1, DELTA contains (D(j) - sigma_I) in its  j-th
component.	If N = 1, then DELTA(1) = 1.  The vector DELTA
contains the information necessary to construct the
(singular) eigenvectors.

RHO

RHO is REAL
The scalar in the symmetric updating formula.

SIGMA

SIGMA is REAL
The computed sigma_I, the I-th updated eigenvalue.

WORK

WORK is REAL array, dimension (N)
If N .ne. 1, WORK contains (D(j) + sigma_I) in its	j-th
component.	If N = 1, then WORK( 1 ) = 1.

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:
November 2011

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

Definition at line 154 of file slasd4.f.

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

Version 3.4.1							  Sun May 26 2013						       slasd4.f(3)```

## Check Out this Related 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

Function/Subroutine Documentation
subroutine slaed4 (integerN, integerI, real, dimension( * )D, real, dimension( * )Z, real, dimension( * )DELTA, realRHO, realDLAM, integerINFO)
SLAED4

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:
November 2011

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 3.4.1							  Sun May 26 2013						       slaed4.f(3)```
Man Page