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slasd8.f(3)				      LAPACK				      slasd8.f(3)

NAME
       slasd8.f -

SYNOPSIS
   Functions/Subroutines
       subroutine slasd8 (ICOMPQ, K, D, Z, VF, VL, DIFL, DIFR, LDDIFR, DSIGMA, WORK, INFO)
	   SLASD8 finds the square roots of the roots of the secular equation, and stores, for
	   each element in D, the distance to its two nearest poles. Used by sbdsdc.

Function/Subroutine Documentation
   subroutine slasd8 (integerICOMPQ, integerK, real, dimension( * )D, real, dimension( * )Z,
       real, dimension( * )VF, real, dimension( * )VL, real, dimension( * )DIFL, real, dimension(
       lddifr, * )DIFR, integerLDDIFR, real, dimension( * )DSIGMA, real, dimension( * )WORK,
       integerINFO)
       SLASD8 finds the square roots of the roots of the secular equation, and stores, for each
       element in D, the distance to its two nearest poles. Used by sbdsdc.

       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.

       Parameters:
	   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 SLASD4.  K >= 1.

	   D

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

	   Z

		     Z is REAL 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 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

		     VL is 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

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

	   DIFR

		     DIFR is 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

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

	   DSIGMA

		     DSIGMA is REAL 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

		     WORK is REAL array, dimension at least 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

       Author:
	   Univ. of Tennessee

	   Univ. of California Berkeley

	   Univ. of Colorado Denver

	   NAG Ltd.

       Date:
	   September 2012

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

       Definition at line 166 of file slasd8.f.

Author
       Generated automatically by Doxygen for LAPACK from the source code.

Version 3.4.2				 Tue Sep 25 2012			      slasd8.f(3)
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