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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,  accumu-
       lating the transformations if desired. Letting B denote the input bidi-
       agonal matrix, the algorithm computes orthogonal matrices Q and P  such
       that  B = Q * S * P' (P' denotes the transpose of P). The singular val-
       ues 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 Guar-
       anteed High Relative Accuracy," by J. Demmel and W. Kahan, LAPACK Work-
       ing 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  sin-
             gular 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  diago-
             nal 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  postmulti-
             plied  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 pre-
             multiplied 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.

