# dlaed5.f

Section: LAPACK (3)
Updated: Tue Nov 14 2017
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dlaed5.f

## SYNOPSIS

### Functions/Subroutines

subroutine dlaed5 (I, D, Z, DELTA, RHO, DLAM)
DLAED5 used by sstedc. Solves the 2-by-2 secular equation.

## Function/Subroutine Documentation

### subroutine dlaed5 (integer I, double precision, dimension( 2 ) D, double precision, dimension( 2 ) Z, double precision, dimension( 2 ) DELTA, double precision RHO, double precision DLAM)

DLAED5 used by sstedc. Solves the 2-by-2 secular equation.

Purpose:

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

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

The diagonal elements in the array D are assumed to satisfy

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 DOUBLE PRECISION array, dimension (2)
The original eigenvalues.  We assume D(1) < D(2).
```

Z

```          Z is DOUBLE PRECISION array, dimension (2)
The components of the updating vector.
```

DELTA

```          DELTA is DOUBLE PRECISION array, dimension (2)
The vector DELTA contains the information necessary
to construct the eigenvectors.
```

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.
```

Author:

Univ. of Tennessee

Univ. of California Berkeley

NAG Ltd.

Date:

December 2016

Contributors:

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

Definition at line 110 of file dlaed5.f.

## Author

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