# dlasd5.f - Man Page

SRC/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.

Contributors:

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

Definition at line 115 of file dlasd5.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page dlasd5(3) is an alias of dlasd5.f(3).

Tue Nov 28 2023 12:08:42 Version 3.12.0 LAPACK