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.

**FURTHER** **DETAILS**

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)