---
name: "dlasd5"
section: "3lapack"
platform: "linux"
package: "liblapack-doc"
version: "3.2.1-8"
release: "Debian 6.0 (Squeeze)"
platforms: ["linux"]
url: "https://new.carta.tech/dlasd5/3lapack"
---

# dlasd5(3lapack)

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

## NAME

DLASD5 - 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.

## FURTHER DETAILS

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