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DLASD7(3S)							    DLASD7(3S)

NAME
     DLASD7 - merge the two sets of singular values together into a single
     sorted set

SYNOPSIS
     SUBROUTINE DLASD7( ICOMPQ, NL, NR, SQRE, K, D, Z, ZW, VF, VFW, VL, VLW,
			ALPHA, BETA, DSIGMA, IDX, IDXP, IDXQ, PERM, GIVPTR,
			GIVCOL, LDGCOL, GIVNUM, LDGNUM, C, S, INFO )

	 INTEGER	GIVPTR, ICOMPQ, INFO, K, LDGCOL, LDGNUM, NL, NR, SQRE

	 DOUBLE		PRECISION ALPHA, BETA, C, S

	 INTEGER	GIVCOL( LDGCOL, * ), IDX( * ), IDXP( * ), IDXQ( * ),
			PERM( * )

	 DOUBLE		PRECISION D( * ), DSIGMA( * ), GIVNUM( LDGNUM, * ),
			VF( * ), VFW( * ), VL( * ), VLW( * ), Z( * ), ZW( * )

IMPLEMENTATION
     These routines are part of the SCSL Scientific Library and can be loaded
     using either the -lscs or the -lscs_mp option.  The -lscs_mp option
     directs the linker to use the multi-processor version of the library.

     When linking to SCSL with -lscs or -lscs_mp, the default integer size is
     4 bytes (32 bits). Another version of SCSL is available in which integers
     are 8 bytes (64 bits).  This version allows the user access to larger
     memory sizes and helps when porting legacy Cray codes.  It can be loaded
     by using the -lscs_i8 option or the -lscs_i8_mp option. A program may use
     only one of the two versions; 4-byte integer and 8-byte integer library
     calls cannot be mixed.

PURPOSE
     DLASD7 merges the two sets of singular values together into a single
     sorted set. Then it tries to deflate the size of the problem. There are
     two ways in which deflation can occur:  when two or more singular values
     are close together or if there is a tiny entry in the Z vector. For each
     such occurrence the order of the related secular equation problem is
     reduced by one.

     DLASD7 is called from DLASD6.

ARGUMENTS
     ICOMPQ  (input) INTEGER
	     Specifies whether singular vectors are to be computed in compact
	     form, as follows:
	     = 0: Compute singular values only.
	     = 1: Compute singular vectors of upper bidiagonal matrix in
	     compact form.

									Page 1

DLASD7(3S)							    DLASD7(3S)

     NL	    (input) INTEGER
	    The row dimension of the upper block. NL >= 1.

     NR	    (input) INTEGER
	    The row dimension of the lower block. NR >= 1.

     SQRE   (input) 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 N = NL + NR + 1 rows and M = N + SQRE >=
	    N columns.

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

     D	    (input/output) DOUBLE PRECISION array, dimension ( N )
	    On entry D contains the singular values of the two submatrices to
	    be combined. On exit D contains the trailing (N-K) updated
	    singular values (those which were deflated) sorted into increasing
	    order.

     Z	    (output) DOUBLE PRECISION array, dimension ( M )
	    On exit Z contains the updating row vector in the secular
	    equation.

     ZW	    (workspace) DOUBLE PRECISION array, dimension ( M )
	    Workspace for Z.

     VF	    (input/output) 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.

     VFW    (workspace) DOUBLE PRECISION array, dimension ( M )
	    Workspace for VF.

     VL	    (input/output) 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.

     VLW    (workspace) DOUBLE PRECISION array, dimension ( M )
	    Workspace for VL.

									Page 2

DLASD7(3S)							    DLASD7(3S)

     ALPHA  (input) DOUBLE PRECISION
	    Contains the diagonal element associated with the added row.

     BETA   (input) DOUBLE PRECISION
	    Contains the off-diagonal element associated with the added row.

	    DSIGMA (output) DOUBLE PRECISION array, dimension ( N ) Contains a
	    copy of the diagonal elements (K-1 singular values and one zero)
	    in the secular equation.

     IDX    (workspace) INTEGER array, dimension ( N )
	    This will contain the permutation used to sort the contents of D
	    into ascending order.

     IDXP   (workspace) INTEGER array, dimension ( N )
	    This will contain the permutation used to place deflated values of
	    D at the end of the array. On output IDXP(2:K)
	    points to the nondeflated D-values and IDXP(K+1:N) points to the
	    deflated singular values.

     IDXQ   (input) INTEGER array, dimension ( N )
	    This contains the permutation which separately sorts the two sub-
	    problems in D into ascending order.	 Note that entries in the
	    first half of this permutation must first be moved one position
	    backward; and entries in the second half must first have NL+1
	    added to their values.

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

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

	    GIVCOL (output) 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 (input) INTEGER The leading dimension of GIVCOL, must be at
	    least N.

	    GIVNUM (output) 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 (input) INTEGER The leading dimension of GIVNUM, must be at
	    least N.

     C	    (output) 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.

									Page 3

DLASD7(3S)							    DLASD7(3S)

     S	    (output) 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.

     INFO   (output) INTEGER
	    = 0:  successful exit.
	    < 0:  if INFO = -i, the i-th argument had an illegal value.

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

SEE ALSO
     INTRO_LAPACK(3S), INTRO_SCSL(3S)

     This man page is available only online.

									Page 4

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