DLASD8(3)      LAPACK routine of NEC Numeric Library Collection      DLASD8(3)



NAME
       DLASD8

SYNOPSIS
       SUBROUTINE DLASD8 (ICOMPQ, K, D, Z, VF, VL, DIFL, DIFR, LDDIFR, DSIGMA,
           WORK, INFO)



PURPOSE
            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 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.

            DLASD8 is called from DLASD6.




ARGUMENTS
           ICOMPQ    (input)
                     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.

           K         (input)
                     K is INTEGER
                     The number of terms in the rational function to be solved
                     by DLASD4.  K >= 1.

           D         (output)
                     D is DOUBLE PRECISION array, dimension ( K )
                     On output, D contains the updated singular values.

           Z         (input/output)
                     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.

           VF        (input/output)
                     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.

           VL        (input/output)
                     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.

           DIFL      (output)
                     DIFL is DOUBLE PRECISION array, dimension ( K )
                     On exit, DIFL(I) = D(I) - DSIGMA(I).

           DIFR      (output)
                     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.

           LDDIFR    (input)
                     LDDIFR is INTEGER
                     The leading dimension of DIFR, must be at least K.

           DSIGMA    (input/output)
                     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.

           WORK      (output)
                     WORK is DOUBLE PRECISION array, dimension at least 3 * K

           INFO      (output)
                     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



LAPACK routine                  31 October 2017                      DLASD8(3)