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slasd5

NAME

SLASD5 - 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)

SYNOPSIS

SUBROUTINE SLASD5(

I, D, Z, DELTA, RHO, DSIGMA, WORK )

    

INTEGER I

    

REAL DSIGMA, RHO

    

REAL 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 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.

ARGUMENTS

I (input) INTEGER

The index of the eigenvalue to be computed. I = 1 or I = 2.

D (input) REAL array, dimension ( 2 )

The original eigenvalues. We assume 0 <= D(1) < D(2).

Z (input) REAL array, dimension ( 2 )

The components of the updating vector.

DELTA (output) REAL array, dimension ( 2 )

Contains (D(j) - lambda_I) in its j-th component. The vector DELTA contains the information necessary to construct the eigenvectors.

RHO (input) REAL

The scalar in the symmetric updating formula.

DSIGMA (output) REAL The computed lambda_I, the I-th updated eigenvalue.

WORK (workspace) REAL 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