slasda(3S)

NAME
     SLASDA - a divide and conquer approach, SLASDA 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 SLASDA( 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, * )

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

IMPLEMENTATION
     These routines are part of the SCSL Scientific Library and can be loaded
     using either the -lscs or the -lscs_mp option.  The -lscs_mp option
     directs the linker to use the multi-processor version of the library.

     When linking to SCSL with -lscs or -lscs_mp, the default integer size is
     4 bytes (32 bits). Another version of SCSL is available in which integers
     are 8 bytes (64 bits).  This version allows the user access to larger
     memory sizes and helps when porting legacy Cray codes.  It can be loaded
     by using the -lscs_i8 option or the -lscs_i8_mp option. A program may use
     only one of the two versions; 4-byte integer and 8-byte integer library
     calls cannot be mixed.

PURPOSE
     Using a divide and conquer approach, SLASDA 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, SLASD0, 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) REAL 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) REAL array, dimension ( M-1 )
            Contains the subdiagonal entries of the bidiagonal matrix.  On
            exit, E has been destroyed.

     U      (output) REAL 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) REAL array,
            dimension ( LDU, SMLSIZ+1 ) if ICOMPQ = 1, and not referenced if
            ICOMPQ = 0. If ICOMPQ = 1, on exit, VT' 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) REAL array, dimension ( LDU, NLVL ),
            where NLVL = floor(log_2 (N/SMLSIZ))).

     DIFR   (output) REAL 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 SLASD8 for details.

     Z      (output) REAL 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) REAL 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) REAL 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) REAL 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) REAL 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) REAL 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, an 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


SEE ALSO
     INTRO_LAPACK(3S), INTRO_SCSL(3S)

     This man page is available only online.