# slasd5.f(3) [centos man page]

```slasd5.f(3)							      LAPACK							       slasd5.f(3)

NAME
slasd5.f -

SYNOPSIS
Functions/Subroutines
subroutine slasd5 (I, D, Z, DELTA, RHO, DSIGMA, WORK)
SLASD5 computes the square root of the i-th eigenvalue of a positive symmetric rank-one modification of a 2-by-2 diagonal matrix. Used
by sbdsdc.

Function/Subroutine Documentation
subroutine slasd5 (integerI, real, dimension( 2 )D, real, dimension( 2 )Z, real, dimension( 2 )DELTA, realRHO, realDSIGMA, real, dimension( 2
)WORK)
SLASD5 computes the square root of the i-th eigenvalue of a positive symmetric rank-one modification of a 2-by-2 diagonal matrix. Used by
sbdsdc.

Purpose:

This subroutine computes the square root of the I-th eigenvalue
of a positive symmetric rank-one modification of a 2-by-2 diagonal
matrix

diag( D ) * diag( D ) +	RHO * Z * transpose(Z) .

The diagonal entries in the array D are assumed to satisfy

0 <= D(i) < D(j)  for  i < j .

We also assume RHO > 0 and that the Euclidean norm of the vector
Z is one.

Parameters:
I

I is INTEGER
The index of the eigenvalue to be computed.  I = 1 or I = 2.

D

D is REAL array, dimension (2)
The original eigenvalues.  We assume 0 <= D(1) < D(2).

Z

Z is REAL array, dimension (2)
The components of the updating vector.

DELTA

DELTA is REAL array, dimension (2)
Contains (D(j) - sigma_I) in its  j-th component.
The vector DELTA contains the information necessary
to construct the eigenvectors.

RHO

RHO is REAL
The scalar in the symmetric updating formula.

DSIGMA

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

WORK

WORK is REAL array, dimension (2)
WORK contains (D(j) + sigma_I) in its  j-th component.

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 117 of file slasd5.f.

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

Version 3.4.2							  Tue Sep 25 2012						       slasd5.f(3)```

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```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 computes the square root of the i-th updated eigenvalue of a positive symmetric rank-one modification to a positive diagonal
matrix. Used by sbdsdc.

Function/Subroutine Documentation
subroutine slasd4 (integerN, integerI, real, dimension( * )D, real, dimension( * )Z, real, dimension( * )DELTA, realRHO, realSIGMA, real,
dimension( * )WORK, integerINFO)
SLASD4 computes the square root of the i-th updated eigenvalue of a positive symmetric rank-one modification to a positive diagonal matrix.
Used by sbdsdc.

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:
September 2012

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 3.4.2							  Tue Sep 25 2012						       slasd4.f(3)```
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