This subroutine computes the I-th eigenvalue of a symmetric rank-one


 modification of a 2-by-2 diagonal matrix


            diag( D )  +  RHO * Z * transpose(Z) .


 The diagonal elements in the array D are assumed to satisfy


            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 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)


         The vector DELTA contains the information necessary


         to construct the eigenvectors.

RHO

          RHO is DOUBLE PRECISION


         The scalar in the symmetric updating formula.

DLAM

          DLAM is DOUBLE PRECISION


         The computed lambda_I, the I-th updated eigenvalue.

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