Provided by: liblapack-doc_3.3.1-1_all #### NAME

```       LAPACK-3  -  subroutine  compute  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
The diagonal entries in the array D are assumed to satisfy   0 <= D(i) < D(j) for i < j

```

#### SYNOPSIS

```       SUBROUTINE DLASD5( I, D, Z, DELTA, RHO, DSIGMA, WORK )

INTEGER        I

DOUBLE         PRECISION DSIGMA, RHO

DOUBLE         PRECISION D( 2 ), DELTA( 2 ), WORK( 2 ), Z( 2 )

```

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

```

#### ARGUMENTS

```        I      (input) INTEGER
The index of the eigenvalue to be computed.  I = 1 or I = 2.

D      (input) DOUBLE PRECISION array, dimension ( 2 )
The original eigenvalues.  We assume 0 <= D(1) < D(2).

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

DELTA  (output) DOUBLE PRECISION 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    (input) DOUBLE PRECISION
The scalar in the symmetric updating formula.
DSIGMA (output) DOUBLE PRECISION
The computed sigma_I, the I-th updated eigenvalue.

WORK   (workspace) DOUBLE PRECISION array, dimension ( 2 )
WORK contains (D(j) + sigma_I) in its  j-th component.

```

#### FURTHERDETAILS

```        Based on contributions by
Ren-Cang Li, Computer Science Division, University of California
at Berkeley, USA

LAPACK auxiliary routine (version 3.2)     April 2011                            DLASD5(3lapack)
```