# dlasd5.f

Section: LAPACK (3)
Updated: Tue Nov 14 2017
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dlasd5.f

## SYNOPSIS

### Functions/Subroutines

subroutine dlasd5 (I, D, Z, DELTA, RHO, DSIGMA, WORK)
DLASD5 computes the square root of the i-th eigenvalue of a positive symmetric rank-one modification of a 2-by-2 diagonal matrix. Used by sbdsdc.

## Function/Subroutine Documentation

### subroutine dlasd5 (integer I, double precision, dimension( 2 ) D, double precision, dimension( 2 ) Z, double precision, dimension( 2 ) DELTA, double precision RHO, double precision DSIGMA, double precision, dimension( 2 ) WORK)

DLASD5 computes the square root of the i-th eigenvalue of a positive symmetric rank-one modification of a 2-by-2 diagonal matrix. Used by sbdsdc.

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

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

The diagonal entries in the array D are assumed to satisfy

0 <= 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 0 <= 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 )
Contains (D(j) - sigma_I) in its  j-th component.
The vector DELTA contains the information necessary
to construct the eigenvectors.
```

RHO

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

DSIGMA

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

WORK

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

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 118 of file dlasd5.f.

## Author

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