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.

     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.

     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.
     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.