!>
!> 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.
!> 

ICOMPQ

!>          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

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

D

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

Z

!>          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

!>          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

!>          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

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

DIFR

!>          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

!>          LDDIFR is INTEGER
!>          The leading dimension of DIFR, must be at least K.
!> 

DSIGMA

!>          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.
!> 

WORK

!>          WORK is DOUBLE PRECISION array, dimension (3*K)
!> 

INFO

!>          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
!> 

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

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