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DLASD8(1)	    LAPACK auxiliary routine (version 3.2)	     DLASD8(1)

NAME
       DLASD8 - finds the square roots of the roots of the secular equation,

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

	   INTEGER	  ICOMPQ, INFO, K, LDDIFR

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

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) INTEGER
	       Specifies whether singular vectors are to be computed  in  fac‐
	       tored 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
	       DLASD4.	K >= 1.

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

       Z       (input/output) DOUBLE PRECISION array, dimension ( K )
	       On entry, the first K elements of this array contain the compo‐
	       nents  of the deflation-adjusted updating row vector.  On exit,
	       Z is updated.

       VF      (input/output) DOUBLE PRECISION array, dimension ( K )
	       On entry, VF contains  information passed through  DBEDE8.   On
	       exit,  VF  contains  the first K components of the first compo‐
	       nents of all right singular vectors of the bidiagonal matrix.

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

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

       DSIGMA  (input/output) 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    (workspace) DOUBLE PRECISION 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 auxiliary routine (versioNovember 2008			     DLASD8(1)
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