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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  val-
       ues 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 com-
               pact 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 increas-
              ing order.

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

       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) con-
              tains 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)  con-
              tains  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 posi-
              tion 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 corre-
              sponding 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 rota-
              tion 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  rota-
              tion 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.

