dlaed4.f -

## SYNOPSIS

### Functions/Subroutines

subroutine dlaed4 (N, I, D, Z, DELTA, RHO, DLAM, INFO)
DLAED4 used by sstedc. Finds a single root of the secular equation.

## Function/Subroutine Documentation

### subroutine dlaed4 (integerN, integerI, double precision, dimension( * )D, double precision, dimension( * )Z, double precision, dimension( * )DELTA, double precisionRHO, double precisionDLAM, integerINFO)

DLAED4 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 DOUBLE PRECISION array, dimension (N)
The original eigenvalues.  It is assumed that they are in
order, 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 .GT. 2, DELTA contains (D(j) - lambda_I) in its  j-th
component.  If N = 1, then DELTA(1) = 1. If N = 2, see DLAED5
for detail. The vector DELTA contains the information necessary
to construct the eigenvectors by DLAED3 and DLAED9.
```

RHO

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

DLAM

```          DLAM is DOUBLE PRECISION
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 dlaed4.f.

## Author

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