# slaed4.f man page

slaed4.f —

## Synopsis

### Functions/Subroutines

subroutineslaed4(N, I, D, Z, DELTA, RHO, DLAM, INFO)SLAED4used 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

Univ. of Colorado Denver

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.

## Referenced By

slaed4(3) is an alias of slaed4.f(3).