ESMF_DLASD5 Subroutine

subroutine ESMF_DLASD5(I, D, Z, DELTA, RHO, DSIGMA, WORK)

\brief \b ESMF_DLASD5 \htmlonly Download ESMF_DLASD5 + dependencies [TGZ] [ZIP] [TXT] \endhtmlonly \par Purpose:

\verbatim

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. \endverbatim \param[in] I \verbatim I is INTEGER The index of the eigenvalue to be computed. I = 1 or I = 2. \endverbatim

\param[in] D \verbatim D is DOUBLE PRECISION array, dimension ( 2 ) The original eigenvalues. We assume 0 <= D(1) < D(2). \endverbatim

\param[in] Z \verbatim Z is DOUBLE PRECISION array, dimension ( 2 ) The components of the updating vector. \endverbatim

\param[out] DELTA \verbatim 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. \endverbatim

\param[in] RHO \verbatim RHO is DOUBLE PRECISION The scalar in the symmetric updating formula. \endverbatim

\param[out] DSIGMA \verbatim DSIGMA is DOUBLE PRECISION The computed sigma_I, the I-th updated eigenvalue. \endverbatim

\param[out] WORK \verbatim WORK is DOUBLE PRECISION array, dimension ( 2 ) WORK contains (D(j) + sigma_I) in its j-th component. \endverbatim \author Univ. of Tennessee \author Univ. of California Berkeley \author Univ. of Colorado Denver \author NAG Ltd. \date November 2011 \ingroup auxOTHERauxiliary \par Contributors:

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

Arguments