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 REAL array, dimension (2)


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

Z

          Z is REAL array, dimension (2)


         The components of the updating vector.

DELTA

          DELTA is REAL 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 REAL


         The scalar in the symmetric updating formula.

DSIGMA

          DSIGMA is REAL


         The computed sigma_I, the I-th updated eigenvalue.

WORK

          WORK is REAL 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