Provided by: liblapack-doc_3.3.1-1_all bug

NAME

       LAPACK-3 - merges 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( * )

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

 LAPACK auxiliary routine (version 3.2)     April 2011                            DLASD7(3lapack)