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 SLASD2( NL, NR, SQRE, K, D, Z, ALPHA, BETA, U, LDU, VT, LDVT, DSIGMA, U2, LDU2,
                          VT2, LDVT2, IDXP, IDX, IDXC, IDXQ, COLTYP, INFO )

           INTEGER        INFO, K, LDU, LDU2, LDVT, LDVT2, NL, NR, SQRE

           REAL           ALPHA, BETA

           INTEGER        COLTYP( * ), IDX( * ), IDXC( * ), IDXP( * ), IDXQ( * )

           REAL           D( * ), DSIGMA( * ), U( LDU, * ), U2( LDU2, * ), VT( LDVT,  *  ),  VT2(
                          LDVT2, * ), Z( * )

PURPOSE

       SLASD2  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.
        SLASD2 is called from SLASD1.

ARGUMENTS

        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) REAL 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) REAL array, dimension (N)
               On exit Z contains the updating row vector in the secular
               equation.

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

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

        U      (input/output) REAL array, dimension (LDU,N)
               On entry U contains the left singular vectors of two
               submatrices in the two square blocks with corners at (1,1),
               (NL, NL), and (NL+2, NL+2), (N,N).
               On exit U contains the trailing (N-K) updated left singular
               vectors (those which were deflated) in its last N-K columns.

        LDU    (input) INTEGER
               The leading dimension of the array U.  LDU >= N.

        VT     (input/output) REAL array, dimension (LDVT,M)
               On entry VT**T contains the right singular vectors of two
               submatrices in the two square blocks with corners at (1,1),
               (NL+1, NL+1), and (NL+2, NL+2), (M,M).
               On exit VT**T contains the trailing (N-K) updated right singular
               vectors (those which were deflated) in its last N-K columns.
               In case SQRE =1, the last row of VT spans the right null
               space.

        LDVT   (input) INTEGER
               The leading dimension of the array VT.  LDVT >= M.
               DSIGMA (output) REAL array, dimension (N)
               Contains a copy of the diagonal elements (K-1 singular values
               and one zero) in the secular equation.

        U2     (output) REAL array, dimension (LDU2,N)
               Contains a copy of the first K-1 left singular vectors which
               will be used by SLASD3 in a matrix multiply (SGEMM) to solve
               for the new left singular vectors. U2 is arranged into four
               blocks. The first block contains a column with 1 at NL+1 and
               zero everywhere else; the second block contains non-zero
               entries only at and above NL; the third contains non-zero
               entries only below NL+1; and the fourth is dense.

        LDU2   (input) INTEGER
               The leading dimension of the array U2.  LDU2 >= N.

        VT2    (output) REAL array, dimension (LDVT2,N)
               VT2**T contains a copy of the first K right singular vectors
               which will be used by SLASD3 in a matrix multiply (SGEMM) to
               solve for the new right singular vectors. VT2 is arranged into
               three blocks. The first block contains a row that corresponds
               to the special 0 diagonal element in SIGMA; the second block
               contains non-zeros only at and before NL +1; the third block
               contains non-zeros only at and after  NL +2.

        LDVT2  (input) INTEGER
               The leading dimension of the array VT2.  LDVT2 >= M.

        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.

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

        IDXC   (output) INTEGER array, dimension (N)
               This will contain the permutation used to arrange the columns
               of the deflated U matrix into three groups:  the first group
               contains non-zero entries only at and above NL, the second
               contains non-zero entries only below NL+2, and the third is
               dense.

        IDXQ   (input/output) 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 hlaf 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.
               COLTYP (workspace/output) INTEGER array, dimension (N)
               As workspace, this will contain a label which will indicate
               which of the following types a column in the U2 matrix or a
               row in the VT2 matrix is:
               1 : non-zero in the upper half only
               2 : non-zero in the lower half only
               3 : dense
               4 : deflated
               On exit, it is an array of dimension 4, with COLTYP(I) being
               the dimension of the I-th type columns.

        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                            SLASD2(3lapack)