slasd0(3S)

NAME
     SLASD0 - a divide and conquer approach, SLASD0 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 SLASD0( N, SQRE, D, E, U, LDU, VT, LDVT, SMLSIZ, IWORK, WORK,
                        INFO )

         INTEGER        INFO, LDU, LDVT, N, SMLSIZ, SQRE

         INTEGER        IWORK( * )

         REAL           D( * ), E( * ), U( LDU, * ), VT( LDVT, * ), WORK( * )

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, SLASD0 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
     orthogonal matrices U and VT such that B = U * S * VT. The singular
     values S are overwritten on D.

     A related subroutine, SLASDA, computes only the singular values, and
     optionally, the singular vectors in compact form.


ARGUMENTS
     N      (input) INTEGER
            On entry, 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 at least (LDQ, N)
            On exit, U contains the left singular vectors.

     LDU    (input) INTEGER
            On entry, leading dimension of U.

     VT     (output) REAL array, dimension at least (LDVT, M)
            On exit, VT' contains the right singular vectors.

     LDVT   (input) INTEGER
            On entry, leading dimension of VT.

            SMLSIZ (input) INTEGER On entry, maximum size of the subproblems
            at the bottom of the computation tree.

     IWORK  (workspace) INTEGER array.
            Dimension must be at least (8 * N)

     WORK   (workspace) REAL array.
            Dimension must be at least (3 * M**2 + 2 * M)

     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.