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dlasd7 examples
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Man Page Details
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NAME
       DLASD7  - 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

