DLASD5(3)      LAPACK routine of NEC Numeric Library Collection      DLASD5(3)



NAME
       DLASD5

SYNOPSIS
       SUBROUTINE DLASD5 (I, D, Z, DELTA, RHO, DSIGMA, WORK)



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

           D         (input)
                     D is DOUBLE PRECISION array, dimension ( 2 )
                    The original eigenvalues.  We assume 0 <= D(1) < D(2).

           Z         (input)
                     Z is DOUBLE PRECISION array, dimension ( 2 )
                    The components of the updating vector.

           DELTA     (output)
                     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       (input)
                     RHO is DOUBLE PRECISION
                    The scalar in the symmetric updating formula.

           DSIGMA    (output)
                     DSIGMA is DOUBLE PRECISION
                    The computed sigma_I, the I-th updated eigenvalue.

           WORK      (output)
                     WORK is DOUBLE PRECISION array, dimension ( 2 )
                    WORK contains (D(j) + sigma_I) in its  j-th component.



LAPACK routine                  31 October 2017                      DLASD5(3)