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

NAME

       LAPACK-3 - a divide and conquer approach, DLASDA computes the singular value decomposition
       (SVD) of a real upper bidiagonal N-by-M matrix B with diagonal D and offdiagonal E,  where
       M = N + SQRE

SYNOPSIS

       SUBROUTINE DLASDA( ICOMPQ,  SMLSIZ,  N,  SQRE,  D, E, U, LDU, VT, K, DIFL, DIFR, Z, POLES,
                          GIVPTR, GIVCOL, LDGCOL, PERM, GIVNUM, C, S, WORK, IWORK, INFO )

           INTEGER        ICOMPQ, INFO, LDGCOL, LDU, N, SMLSIZ, SQRE

           INTEGER        GIVCOL( LDGCOL, * ), GIVPTR( * ), IWORK( * ), K( * ), PERM( LDGCOL, * )

           DOUBLE         PRECISION C( * ), D( * ), DIFL( LDU, * ), DIFR(  LDU,  *  ),  E(  *  ),
                          GIVNUM(  LDU,  * ), POLES( LDU, * ), S( * ), U( LDU, * ), VT( LDU, * ),
                          WORK( * ), Z( LDU, * )

PURPOSE

       Using a divide and conquer approach, DLASDA  computes  the  singular  value  decomposition
       (SVD)  of a real upper bidiagonal N-by-M matrix B with diagonal D and offdiagonal E, where
       M = N + SQRE. The
        algorithm computes the singular values in the SVD B = U * S * VT.
        The orthogonal matrices U and VT are optionally computed in
        compact form.
        A related subroutine, DLASD0, computes the singular values and
        the singular vectors in explicit form.

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.
        SMLSIZ (input) INTEGER
        The maximum size of the subproblems at the bottom of the
        computation tree.

        N      (input) INTEGER
               The row dimension of the upper bidiagonal matrix. This is
               also the dimension of the main diagonal array D.

        SQRE   (input) INTEGER
               Specifies the column dimension of the bidiagonal matrix.
               = 0: The bidiagonal matrix has column dimension M = N;
               = 1: The bidiagonal matrix has column dimension M = N + 1.

        D      (input/output) DOUBLE PRECISION array, dimension ( N )
               On entry D contains the main diagonal of the bidiagonal
               matrix. On exit D, if INFO = 0, contains its singular values.

        E      (input) DOUBLE PRECISION array, dimension ( M-1 )
               Contains the subdiagonal entries of the bidiagonal matrix.
               On exit, E has been destroyed.

        U      (output) DOUBLE PRECISION array,
               dimension ( LDU, SMLSIZ ) if ICOMPQ = 1, and not referenced
               if ICOMPQ = 0. If ICOMPQ = 1, on exit, U contains the left
               singular vector matrices of all subproblems at the bottom
               level.

        LDU    (input) INTEGER, LDU = > N.
               The leading dimension of arrays U, VT, DIFL, DIFR, POLES,
               GIVNUM, and Z.

        VT     (output) DOUBLE PRECISION array,
               dimension ( LDU, SMLSIZ+1 ) if ICOMPQ = 1, and not referenced
               if ICOMPQ = 0. If ICOMPQ = 1, on exit, VT**T contains the right
               singular vector matrices of all subproblems at the bottom
               level.

        K      (output) INTEGER array,
               dimension ( N ) if ICOMPQ = 1 and dimension 1 if ICOMPQ = 0.
               If ICOMPQ = 1, on exit, K(I) is the dimension of the I-th
               secular equation on the computation tree.

        DIFL   (output) DOUBLE PRECISION array, dimension ( LDU, NLVL ),
               where NLVL = floor(log_2 (N/SMLSIZ))).

        DIFR   (output) DOUBLE PRECISION array,
               dimension ( LDU, 2 * NLVL ) if ICOMPQ = 1 and
               dimension ( N ) if ICOMPQ = 0.
               If ICOMPQ = 1, on exit, DIFL(1:N, I) and DIFR(1:N, 2 * I - 1)
               record distances between singular values on the I-th
               level and singular values on the (I -1)-th level, and
               DIFR(1:N, 2 * I ) contains the normalizing factors for
               the right singular vector matrix. See DLASD8 for details.

        Z      (output) DOUBLE PRECISION array,
               dimension ( LDU, NLVL ) if ICOMPQ = 1 and
               dimension ( N ) if ICOMPQ = 0.
               The first K elements of Z(1, I) contain the components of
               the deflation-adjusted updating row vector for subproblems
               on the I-th level.

        POLES  (output) DOUBLE PRECISION array,
               dimension ( LDU, 2 * NLVL ) if ICOMPQ = 1, and not referenced
               if ICOMPQ = 0. If ICOMPQ = 1, on exit, POLES(1, 2*I - 1) and
               POLES(1, 2*I) contain  the new and old singular values
               involved in the secular equations on the I-th level.
               GIVPTR (output) INTEGER array,
               dimension ( N ) if ICOMPQ = 1, and not referenced if
               ICOMPQ = 0. If ICOMPQ = 1, on exit, GIVPTR( I ) records
               the number of Givens rotations performed on the I-th
               problem on the computation tree.
               GIVCOL (output) INTEGER array,
               dimension ( LDGCOL, 2 * NLVL ) if ICOMPQ = 1, and not
               referenced if ICOMPQ = 0. If ICOMPQ = 1, on exit, for each I,
               GIVCOL(1, 2 *I - 1) and GIVCOL(1, 2 *I) record the locations
               of Givens rotations performed on the I-th level on the
               computation tree.
               LDGCOL (input) INTEGER, LDGCOL = > N.
               The leading dimension of arrays GIVCOL and PERM.

        PERM   (output) INTEGER array,
               dimension ( LDGCOL, NLVL ) if ICOMPQ = 1, and not referenced
               if ICOMPQ = 0. If ICOMPQ = 1, on exit, PERM(1, I) records
               permutations done on the I-th level of the computation tree.
               GIVNUM (output) DOUBLE PRECISION array,
               dimension ( LDU,  2 * NLVL ) if ICOMPQ = 1, and not
               referenced if ICOMPQ = 0. If ICOMPQ = 1, on exit, for each I,
               GIVNUM(1, 2 *I - 1) and GIVNUM(1, 2 *I) record the C- and S-
               values of Givens rotations performed on the I-th level on
               the computation tree.

        C      (output) DOUBLE PRECISION array,
               dimension ( N ) if ICOMPQ = 1, and dimension 1 if ICOMPQ = 0.
               If ICOMPQ = 1 and the I-th subproblem is not square, on exit,
               C( I ) contains the C-value of a Givens rotation related to
               the right null space of the I-th subproblem.

        S      (output) DOUBLE PRECISION array, dimension ( N ) if
               ICOMPQ = 1, and dimension 1 if ICOMPQ = 0. If ICOMPQ = 1
               and the I-th subproblem is not square, on exit, S( I )
               contains the S-value of a Givens rotation related to
               the right null space of the I-th subproblem.

        WORK   (workspace) DOUBLE PRECISION array, dimension
               (6 * N + (SMLSIZ + 1)*(SMLSIZ + 1)).

        IWORK  (workspace) INTEGER array.
               Dimension must be at least (7 * N).

        INFO   (output) INTEGER
               = 0:  successful exit.
               < 0:  if INFO = -i, the i-th argument had an illegal value.
               > 0:  if INFO = 1, a singular value did not converge

FURTHER DETAILS

        Based on contributions by
           Ming Gu and Huan Ren, Computer Science Division, University of
           California at Berkeley, USA

 LAPACK auxiliary routine (version 3.2.2)   April 2011                            DLASDA(3lapack)