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

NAME

       LAPACK-3  -  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

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( * )

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**T (P**T 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**T * VT if desired.
        The input matrix C  is changed to Q**T * 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**T, 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**T  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

 LAPACK auxiliary routine (version 3.2)     April 2011                            SLASDQ(3lapack)