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dlasdq examples
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Man Page Details
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NAME
       DLASDQ  -  the  singular  value decomposition (SVD) of a real (upper or
       lower) bidiagonal matrix with diagonal D and offdiagonal E,  accumulat-
       ing the transformations if desired

SYNOPSIS
       SUBROUTINE DLASDQ( 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

           DOUBLE         PRECISION C( LDC, * ), D( * ), E( * ), U( LDU, *  ),
                          VT( LDVT, * ), WORK( * )

  Purpose
  =======

  DLASDQ 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) DOUBLE PRECISION 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) DOUBLE PRECISION 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) DOUBLE PRECISION 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) DOUBLE PRECISION 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) DOUBLE PRECISION 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) DOUBLE PRECISION 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

