SLASD8(l)								 )								 SLASD8(l)

NAME

       SLASD8 - find the square roots of the roots of the secular equation,

SYNOPSIS

       SUBROUTINE SLASD8( ICOMPQ, K, D, Z, VF, VL, DIFL, DIFR, LDDIFR, DSIGMA, WORK, INFO )

	   INTEGER	  ICOMPQ, INFO, K, LDDIFR

	   REAL 	  D( * ), DIFL( * ), DIFR( LDDIFR, * ), DSIGMA( * ), VF( * ), VL( * ), WORK( * ), Z( * )

PURPOSE

       SLASD8  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 SLASD4, 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.

       SLASD8 is called from SLASD6.

ARGUMENTS

       ICOMPQ  (input) 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) INTEGER
	       The number of terms in the rational function to be solved by SLASD4.  K >= 1.

       D       (output) REAL array, dimension ( K )
	       On output, D contains the updated singular values.

       Z       (input) REAL array, dimension ( K )
	       The first K elements of this array contain the components of the deflation-adjusted updating row vector.

       VF      (input/output) REAL 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) REAL 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) REAL array, dimension ( K )
	       On exit, DIFL(I) = D(I) - DSIGMA(I).

       DIFR    (output) REAL 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) INTEGER
	       The leading dimension of DIFR, must be at least K.

       DSIGMA  (input) REAL array, dimension ( K )
	       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    (workspace) REAL array, dimension at least 3 * K

       INFO    (output) INTEGER
	       = 0:  successful exit.
	       < 0:  if INFO = -i, the i-th argument had an illegal value.
	       > 0:  if INFO = 1, an singular value did not converge

FURTHER DETAILS

       Based on contributions by
	  Ming Gu and Huan Ren, Computer Science Division, University of
	  California at Berkeley, USA

LAPACK version 3.0						   15 June 2000 							 SLASD8(l)