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dlasd6.f(3)				      LAPACK				      dlasd6.f(3)

NAME
       dlasd6.f -

SYNOPSIS
   Functions/Subroutines
       subroutine dlasd6 (ICOMPQ, NL, NR, SQRE, D, VF, VL, ALPHA, BETA, IDXQ, PERM, GIVPTR,
	   GIVCOL, LDGCOL, GIVNUM, LDGNUM, POLES, DIFL, DIFR, Z, K, C, S, WORK, IWORK, INFO)
	   DLASD6 computes the SVD of an updated upper bidiagonal matrix obtained by merging two
	   smaller ones by appending a row. Used by sbdsdc.

Function/Subroutine Documentation
   subroutine dlasd6 (integerICOMPQ, integerNL, integerNR, integerSQRE, double precision,
       dimension( * )D, double precision, dimension( * )VF, double precision, dimension( * )VL,
       double precisionALPHA, double precisionBETA, integer, dimension( * )IDXQ, integer,
       dimension( * )PERM, integerGIVPTR, integer, dimension( ldgcol, * )GIVCOL, integerLDGCOL,
       double precision, dimension( ldgnum, * )GIVNUM, integerLDGNUM, double precision,
       dimension( ldgnum, * )POLES, double precision, dimension( * )DIFL, double precision,
       dimension( * )DIFR, double precision, dimension( * )Z, integerK, double precisionC, double
       precisionS, double precision, dimension( * )WORK, integer, dimension( * )IWORK,
       integerINFO)
       DLASD6 computes the SVD of an updated upper bidiagonal matrix obtained by merging two
       smaller ones by appending a row. Used by sbdsdc.

       Purpose:

	    DLASD6 computes the SVD of an updated upper bidiagonal matrix B
	    obtained by merging two smaller ones by appending a row. This
	    routine is used only for the problem which requires all singular
	    values and optionally singular vector matrices in factored form.
	    B is an N-by-M matrix with N = NL + NR + 1 and M = N + SQRE.
	    A related subroutine, DLASD1, handles the case in which all singular
	    values and singular vectors of the bidiagonal matrix are desired.

	    DLASD6 computes the SVD as follows:

			  ( D1(in)    0    0	   0 )
	      B = U(in) * (   Z1**T   a   Z2**T    b ) * VT(in)
			  (   0       0   D2(in)   0 )

		= U(out) * ( D(out) 0) * VT(out)

	    where Z**T = (Z1**T a Z2**T b) = u**T VT**T, and u is a vector of dimension M
	    with ALPHA and BETA in the NL+1 and NL+2 th entries and zeros
	    elsewhere; and the entry b is empty if SQRE = 0.

	    The singular values of B can be computed using D1, D2, the first
	    components of all the right singular vectors of the lower block, and
	    the last components of all the right singular vectors of the upper
	    block. These components are stored and updated in VF and VL,
	    respectively, in DLASD6. Hence U and VT are not explicitly
	    referenced.

	    The singular values are stored in D. The algorithm consists of two
	    stages:

		  The first stage consists of deflating the size of the problem
		  when there are multiple singular values or if there is a zero
		  in the Z vector. For each such occurence the dimension of the
		  secular equation problem is reduced by one. This stage is
		  performed by the routine DLASD7.

		  The second stage consists of calculating the updated
		  singular values. This is done by finding the roots of the
		  secular equation via the routine DLASD4 (as called by DLASD8).
		  This routine also updates VF and VL and computes the distances
		  between the updated singular values and the old singular
		  values.

	    DLASD6 is called from DLASDA.

       Parameters:
	   ICOMPQ

		     ICOMPQ is INTEGER
		    Specifies whether singular vectors are to be computed in
		    factored form:
		    = 0: Compute singular values only.
		    = 1: Compute singular vectors in factored form as well.

	   NL

		     NL is INTEGER
		    The row dimension of the upper block.  NL >= 1.

	   NR

		     NR is INTEGER
		    The row dimension of the lower block.  NR >= 1.

	   SQRE

		     SQRE is INTEGER
		    = 0: the lower block is an NR-by-NR square matrix.
		    = 1: the lower block is an NR-by-(NR+1) rectangular matrix.

		    The bidiagonal matrix has row dimension N = NL + NR + 1,
		    and column dimension M = N + SQRE.

	   D

		     D is DOUBLE PRECISION array, dimension ( NL+NR+1 ).
		    On entry D(1:NL,1:NL) contains the singular values of the
		    upper block, and D(NL+2:N) contains the singular values
		    of the lower block. On exit D(1:N) contains the singular
		    values of the modified matrix.

	   VF

		     VF is DOUBLE PRECISION array, dimension ( M )
		    On entry, VF(1:NL+1) contains the first components of all
		    right singular vectors of the upper block; and VF(NL+2:M)
		    contains the first components of all right singular vectors
		    of the lower block. On exit, VF contains the first components
		    of all right singular vectors of the bidiagonal matrix.

	   VL

		     VL is DOUBLE PRECISION array, dimension ( M )
		    On entry, VL(1:NL+1) contains the  last components of all
		    right singular vectors of the upper block; and VL(NL+2:M)
		    contains the last components of all right singular vectors of
		    the lower block. On exit, VL contains the last components of
		    all right singular vectors of the bidiagonal matrix.

	   ALPHA

		     ALPHA is DOUBLE PRECISION
		    Contains the diagonal element associated with the added row.

	   BETA

		     BETA is DOUBLE PRECISION
		    Contains the off-diagonal element associated with the added
		    row.

	   IDXQ

		     IDXQ is INTEGER array, dimension ( N )
		    This contains the permutation which will reintegrate the
		    subproblem just solved back into sorted order, i.e.
		    D( IDXQ( I = 1, N ) ) will be in ascending order.

	   PERM

		     PERM is INTEGER array, dimension ( N )
		    The permutations (from deflation and sorting) to be applied
		    to each block. Not referenced if ICOMPQ = 0.

	   GIVPTR

		     GIVPTR is INTEGER
		    The number of Givens rotations which took place in this
		    subproblem. Not referenced if ICOMPQ = 0.

	   GIVCOL

		     GIVCOL is INTEGER array, dimension ( LDGCOL, 2 )
		    Each pair of numbers indicates a pair of columns to take place
		    in a Givens rotation. Not referenced if ICOMPQ = 0.

	   LDGCOL

		     LDGCOL is INTEGER
		    leading dimension of GIVCOL, must be at least N.

	   GIVNUM

		     GIVNUM is DOUBLE PRECISION array, dimension ( LDGNUM, 2 )
		    Each number indicates the C or S value to be used in the
		    corresponding Givens rotation. Not referenced if ICOMPQ = 0.

	   LDGNUM

		     LDGNUM is INTEGER
		    The leading dimension of GIVNUM and POLES, must be at least N.

	   POLES

		     POLES is DOUBLE PRECISION array, dimension ( LDGNUM, 2 )
		    On exit, POLES(1,*) is an array containing the new singular
		    values obtained from solving the secular equation, and
		    POLES(2,*) is an array containing the poles in the secular
		    equation. Not referenced if ICOMPQ = 0.

	   DIFL

		     DIFL is DOUBLE PRECISION array, dimension ( N )
		    On exit, DIFL(I) is the distance between I-th updated
		    (undeflated) singular value and the I-th (undeflated) old
		    singular value.

	   DIFR

		     DIFR is DOUBLE PRECISION array,
			     dimension ( LDGNUM, 2 ) if ICOMPQ = 1 and
			     dimension ( N ) if ICOMPQ = 0.
		    On exit, DIFR(I, 1) is the distance between I-th updated
		    (undeflated) singular value and the I+1-th (undeflated) old
		    singular value.

		    If ICOMPQ = 1, DIFR(1:K,2) is an array containing the
		    normalizing factors for the right singular vector matrix.

		    See DLASD8 for details on DIFL and DIFR.

	   Z

		     Z is DOUBLE PRECISION array, dimension ( M )
		    The first elements of this array contain the components
		    of the deflation-adjusted updating row vector.

	   K

		     K is INTEGER
		    Contains the dimension of the non-deflated matrix,
		    This is the order of the related secular equation. 1 <= K <=N.

	   C

		     C is DOUBLE PRECISION
		    C contains garbage if SQRE =0 and the C-value of a Givens
		    rotation related to the right null space if SQRE = 1.

	   S

		     S is DOUBLE PRECISION
		    S contains garbage if SQRE =0 and the S-value of a Givens
		    rotation related to the right null space if SQRE = 1.

	   WORK

		     WORK is DOUBLE PRECISION array, dimension ( 4 * M )

	   IWORK

		     IWORK is INTEGER array, dimension ( 3 * N )

	   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 312 of file dlasd6.f.

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

Version 3.4.2				 Tue Sep 25 2012			      dlasd6.f(3)
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