SLASD5(3)      LAPACK routine of NEC Numeric Library Collection      SLASD5(3)



NAME
       SLASD5

SYNOPSIS
       SUBROUTINE SLASD5 (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 REAL array, dimension (2)
                    The original eigenvalues.  We assume 0 <= D(1) < D(2).

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

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

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

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



LAPACK routine                  31 October 2017                      SLASD5(3)