# dlasd4.f - Man Page

SRC/dlasd4.f

## Synopsis

### Functions/Subroutines

subroutine dlasd4 (n, i, d, z, delta, rho, sigma, work, info)
DLASD4 computes the square root of the i-th updated eigenvalue of a positive symmetric rank-one modification to a positive diagonal matrix. Used by dbdsdc.

## Function/Subroutine Documentation

### subroutine dlasd4 (integer n, integer i, double precision, dimension( * ) d, double precision, dimension( * ) z, double precision, dimension( * ) delta, double precision rho, double precision sigma, double precision, dimension( * ) work, integer info)

DLASD4 computes the square root of the i-th updated eigenvalue of a positive symmetric rank-one modification to a positive diagonal matrix. Used by dbdsdc.

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 DOUBLE PRECISION 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 DOUBLE PRECISION array, dimension ( N )
The components of the updating vector.```

DELTA

```          DELTA is DOUBLE PRECISION 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 DOUBLE PRECISION
The scalar in the symmetric updating formula.```

SIGMA

```          SIGMA is DOUBLE PRECISION
The computed sigma_I, the I-th updated eigenvalue.```

WORK

```          WORK is DOUBLE PRECISION 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.

Contributors:

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

Definition at line 152 of file dlasd4.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page dlasd4(3) is an alias of dlasd4.f(3).

Tue Nov 28 2023 12:08:42 Version 3.12.0 LAPACK