ESMF_DLASD8 Subroutine

subroutine ESMF_DLASD8(ICOMPQ, K, D, Z, VF, VL, DIFL, DIFR, LDDIFR, DSIGMA, WORK, INFO)

\brief \b ESMF_DLASD8 \htmlonly Download ESMF_DLASD8 + dependencies [TGZ] [ZIP] [TXT] \endhtmlonly \par Purpose:

\verbatim

ESMF_DLASD8 finds the square roots of the roots of the secular equation, as defined by the values in DSIGMA and Z. It makes the appropriate calls to ESMF_DLASD4, and stores, for each element in D, the distance to its two nearest poles (elements in DSIGMA). It also updates the arrays VF and VL, the first and last components of all the right singular vectors of the original bidiagonal matrix.

ESMF_DLASD8 is called from ESMF_DLASD6. \endverbatim \param[in] ICOMPQ \verbatim ICOMPQ is INTEGER Specifies whether singular vectors are to be computed in factored form in the calling routine: = 0: Compute singular values only. = 1: Compute singular vectors in factored form as well. \endverbatim

\param[in] K \verbatim K is INTEGER The number of terms in the rational function to be solved by ESMF_DLASD4. K >= 1. \endverbatim

\param[out] D \verbatim D is DOUBLE PRECISION array, dimension ( K ) On output, D contains the updated singular values. \endverbatim

\param[in,out] Z \verbatim Z is DOUBLE PRECISION array, dimension ( K ) On entry, the first K elements of this array contain the components of the deflation-adjusted updating row vector. On exit, Z is updated. \endverbatim

\param[in,out] VF \verbatim VF is DOUBLE PRECISION array, dimension ( K ) On entry, VF contains information passed through DBEDE8. On exit, VF contains the first K components of the first components of all right singular vectors of the bidiagonal matrix. \endverbatim

\param[in,out] VL \verbatim VL is DOUBLE PRECISION array, dimension ( K ) On entry, VL contains information passed through DBEDE8. On exit, VL contains the first K components of the last components of all right singular vectors of the bidiagonal matrix. \endverbatim

\param[out] DIFL \verbatim DIFL is DOUBLE PRECISION array, dimension ( K ) On exit, DIFL(I) = D(I) - DSIGMA(I). \endverbatim

\param[out] DIFR \verbatim DIFR is DOUBLE PRECISION array, dimension ( LDDIFR, 2 ) if ICOMPQ = 1 and dimension ( K ) if ICOMPQ = 0. On exit, DIFR(I,1) = D(I) - DSIGMA(I+1), DIFR(K,1) is not defined and will not be referenced.

     If ICOMPQ = 1, DIFR(1:K,2) is an array containing the
     normalizing factors for the right singular vector matrix.

\endverbatim

\param[in] LDDIFR \verbatim LDDIFR is INTEGER The leading dimension of DIFR, must be at least K. \endverbatim

\param[in,out] DSIGMA \verbatim DSIGMA is DOUBLE PRECISION array, dimension ( K ) On entry, the first K elements of this array contain the old roots of the deflated updating problem. These are the poles of the secular equation. On exit, the elements of DSIGMA may be very slightly altered in value. \endverbatim

\param[out] WORK \verbatim WORK is DOUBLE PRECISION array, dimension at least 3 * K \endverbatim

\param[out] INFO \verbatim INFO is INTEGER = 0: successful exit. < 0: if INFO = -i, the i-th argument had an illegal value. > 0: if INFO = 1, a singular value did not converge \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:

Ming Gu and Huan Ren, Computer Science Division, University of
California at Berkeley, USA

Arguments