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.

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.

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

September 2012

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