slasdq(3S)

NAME
     SLASDQ - compute the singular value decomposition (SVD) of a real (upper
     or lower) bidiagonal matrix with diagonal D and offdiagonal E,
     accumulating the transformations if desired

SYNOPSIS
     SUBROUTINE SLASDQ( UPLO, SQRE, N, NCVT, NRU, NCC, D, E, VT, LDVT, U, LDU,
                        C, LDC, WORK, INFO )

         CHARACTER      UPLO

         INTEGER        INFO, LDC, LDU, LDVT, N, NCC, NCVT, NRU, SQRE

         REAL           C( LDC, * ), 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
     SLASDQ computes the singular value decomposition (SVD) of a real (upper
     or lower) bidiagonal matrix with diagonal D and offdiagonal E,
     accumulating the transformations if desired. Letting B denote the input
     bidiagonal matrix, the algorithm computes orthogonal matrices Q and P
     such that B = Q * S * P' (P' denotes the transpose of P). The singular
     values S are overwritten on D.

     The input matrix U  is changed to U  * Q  if desired.
     The input matrix VT is changed to P' * VT if desired.
     The input matrix C  is changed to Q' * C  if desired.

     See "Computing  Small Singular Values of Bidiagonal Matrices With
     Guaranteed High Relative Accuracy," by J. Demmel and W. Kahan, LAPACK
     Working Note #3, for a detailed description of the algorithm.


ARGUMENTS
     UPLO  (input) CHARACTER*1
           On entry, UPLO specifies whether the input bidiagonal matrix is
           upper or lower bidiagonal, and wether it is square are not.  UPLO =
           'U' or 'u'   B is upper bidiagonal.  UPLO = 'L' or 'l'   B is lower
           bidiagonal.
     SQRE  (input) INTEGER
           = 0: then the input matrix is N-by-N.
           = 1: then the input matrix is N-by-(N+1) if UPLU = 'U' and (N+1)-
           by-N if UPLU = 'L'.

           The bidiagonal matrix has N = NL + NR + 1 rows and M = N + SQRE >=
           N columns.

     N     (input) INTEGER
           On entry, N specifies the number of rows and columns in the matrix.
           N must be at least 0.

     NCVT  (input) INTEGER
           On entry, NCVT specifies the number of columns of the matrix VT.
           NCVT must be at least 0.

     NRU   (input) INTEGER
           On entry, NRU specifies the number of rows of the matrix U. NRU
           must be at least 0.

     NCC   (input) INTEGER
           On entry, NCC specifies the number of columns of the matrix C. NCC
           must be at least 0.

     D     (input/output) REAL array, dimension (N)
           On entry, D contains the diagonal entries of the bidiagonal matrix
           whose SVD is desired. On normal exit, D contains the singular
           values in ascending order.

     E     (input/output) REAL array.
           dimension is (N-1) if SQRE = 0 and N if SQRE = 1.  On entry, the
           entries of E contain the offdiagonal entries of the bidiagonal
           matrix whose SVD is desired. On normal exit, E will contain 0. If
           the algorithm does not converge, D and E will contain the diagonal
           and superdiagonal entries of a bidiagonal matrix orthogonally
           equivalent to the one given as input.

     VT    (input/output) REAL array, dimension (LDVT, NCVT)
           On entry, contains a matrix which on exit has been premultiplied by
           P', dimension N-by-NCVT if SQRE = 0 and (N+1)-by-NCVT if SQRE = 1
           (not referenced if NCVT=0).

     LDVT  (input) INTEGER
           On entry, LDVT specifies the leading dimension of VT as declared in
           the calling (sub) program. LDVT must be at least 1. If NCVT is
           nonzero LDVT must also be at least N.

     U     (input/output) REAL array, dimension (LDU, N)
           On entry, contains a  matrix which on exit has been postmultiplied
           by Q, dimension NRU-by-N if SQRE = 0 and NRU-by-(N+1) if SQRE = 1
           (not referenced if NRU=0).

     LDU   (input) INTEGER
           On entry, LDU  specifies the leading dimension of U as declared in
           the calling (sub) program. LDU must be at least max( 1, NRU ) .

     C     (input/output) REAL array, dimension (LDC, NCC)
           On entry, contains an N-by-NCC matrix which on exit has been
           premultiplied by Q'  dimension N-by-NCC if SQRE = 0 and (N+1)-by-
           NCC if SQRE = 1 (not referenced if NCC=0).

     LDC   (input) INTEGER
           On entry, LDC  specifies the leading dimension of C as declared in
           the calling (sub) program. LDC must be at least 1. If NCC is
           nonzero, LDC must also be at least N.

     WORK  (workspace) REAL array, dimension (4*N)
           Workspace. Only referenced if one of NCVT, NRU, or NCC is nonzero,
           and if N is at least 2.

     INFO  (output) INTEGER
           On exit, a value of 0 indicates a successful exit.  If INFO < 0,
           argument number -INFO is illegal.  If INFO > 0, the algorithm did
           not converge, and INFO specifies how many superdiagonals 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)

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