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dlasda examples
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Man Page Details
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NAME
       DLASDA  -  divide  and  conquer  approach, DLASDA 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 DLASDA( ICOMPQ,  SMLSIZ, N, SQRE, D, E, U, LDU, VT, K, DIFL,
                          DIFR,  Z,  POLES,  GIVPTR,  GIVCOL,  LDGCOL,   PERM,
                          GIVNUM, C, S, WORK, IWORK, INFO )

           INTEGER        ICOMPQ, INFO, LDGCOL, LDU, N, SMLSIZ, SQRE

           INTEGER        GIVCOL(  LDGCOL,  * ), GIVPTR( * ), IWORK( * ), K( *
                          ), PERM( LDGCOL, * )

           DOUBLE         PRECISION C( * ), D( * ), DIFL( LDU, * ), DIFR( LDU,
                          * ), E( * ), GIVNUM( LDU, * ), POLES( LDU, * ), S( *
                          ), U( LDU, * ), VT( LDU, * ), WORK( * ), Z( LDU, * )

PURPOSE
       Using a divide and conquer approach, DLASDA 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 com-
       putes the singular values in the SVD B = U * S *  VT.   The  orthogonal
       matrices U and VT are optionally computed in compact form.

       A related subroutine, DLASD0, computes the singular values and the sin-
       gular vectors in explicit form.


ARGUMENTS
       ICOMPQ (input) INTEGER Specifies whether singular  vectors  are  to  be
       computed in compact form, as follows = 0: Compute singular values only.
       = 1: Compute singular vectors of upper  bidiagonal  matrix  in  compact
       form.

       SMLSIZ  (input) INTEGER The maximum size of the subproblems at the bot-
       tom of the computation tree.

       N      (input) INTEGER
              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) DOUBLE PRECISION 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) DOUBLE PRECISION array, dimension ( M-1 )
              Contains  the  subdiagonal entries of the bidiagonal matrix.  On
              exit, E has been destroyed.

       U      (output) DOUBLE PRECISION array,
              dimension ( LDU, SMLSIZ ) if ICOMPQ = 1, and not  referenced  if
              ICOMPQ = 0. If ICOMPQ = 1, on exit, U contains the left singular
              vector matrices of all subproblems at the bottom level.

       LDU    (input) INTEGER, LDU = > N.
              The leading dimension  of  arrays  U,  VT,  DIFL,  DIFR,  POLES,
              GIVNUM, and Z.

       VT     (output) DOUBLE PRECISION array,
              dimension ( LDU, SMLSIZ+1 ) if ICOMPQ = 1, and not referenced if
              ICOMPQ = 0. If ICOMPQ = 1, on exit, VT' contains the right  sin-
              gular vector matrices of all subproblems at the bottom level.

       K      (output) INTEGER array,
              dimension ( N ) if ICOMPQ = 1 and dimension 1 if ICOMPQ = 0.  If
              ICOMPQ = 1, on exit, K(I) is the dimension of the  I-th  secular
              equation on the computation tree.

       DIFL   (output) DOUBLE PRECISION array, dimension ( LDU, NLVL ),
              where NLVL = floor(log_2 (N/SMLSIZ))).

       DIFR   (output) DOUBLE PRECISION array,
              dimension ( LDU, 2 * NLVL ) if ICOMPQ = 1 and dimension ( N ) if
              ICOMPQ = 0.  If ICOMPQ = 1, on exit, DIFL(1:N, I) and  DIFR(1:N,
              2  * I - 1) record distances between singular values on the I-th
              level and singular values on the (I -1)-th level, and  DIFR(1:N,
              2  * I ) contains the normalizing factors for the right singular
              vector matrix. See DLASD8 for details.

       Z      (output) DOUBLE PRECISION array,
              dimension ( LDU, NLVL ) if ICOMPQ = 1 and dimension  (  N  )  if
              ICOMPQ  = 0.  The first K elements of Z(1, I) contain the compo-
              nents of the deflation-adjusted updating row vector for subprob-
              lems on the I-th level.

       POLES  (output) DOUBLE PRECISION array,
              dimension ( LDU, 2 * NLVL ) if ICOMPQ = 1, and not referenced if
              ICOMPQ = 0. If ICOMPQ = 1,  on  exit,  POLES(1,  2*I  -  1)  and
              POLES(1,  2*I) contain  the new and old singular values involved
              in the secular equations on the I-th level.

              GIVPTR (output) INTEGER array, dimension ( N ) if  ICOMPQ  =  1,
              and  not  referenced  if  ICOMPQ  =  0.  If ICOMPQ = 1, on exit,
              GIVPTR( I ) records the number of Givens rotations performed  on
              the I-th problem on the computation tree.

              GIVCOL (output) INTEGER array, dimension ( LDGCOL, 2 * NLVL ) if
              ICOMPQ = 1, and not referenced if ICOMPQ = 0. If ICOMPQ = 1,  on
              exit, for each I, GIVCOL(1, 2 *I - 1) and GIVCOL(1, 2 *I) record
              the locations of Givens rotations performed on the I-th level on
              the computation tree.

              LDGCOL  (input) INTEGER, LDGCOL = > N.  The leading dimension of
              arrays GIVCOL and PERM.

       PERM   (output) INTEGER array,
              dimension ( LDGCOL, NLVL ) if ICOMPQ = 1, and not referenced  if
              ICOMPQ  = 0. If ICOMPQ = 1, on exit, PERM(1, I) records permuta-
              tions done on the I-th level of the computation tree.

              GIVNUM (output) DOUBLE PRECISION array, dimension (  LDU,   2  *
              NLVL  )  if  ICOMPQ  =  1,  and not referenced if ICOMPQ = 0. If
              ICOMPQ = 1, on exit, for  each  I,  GIVNUM(1,  2  *I  -  1)  and
              GIVNUM(1,  2 *I) record the C- and S- values of Givens rotations
              performed on the I-th level on the computation tree.

       C      (output) DOUBLE PRECISION array,
              dimension ( N ) if ICOMPQ = 1, and dimension 1 if  ICOMPQ  =  0.
              If ICOMPQ = 1 and the I-th subproblem is not square, on exit, C(
              I ) contains the C-value of a Givens  rotation  related  to  the
              right null space of the I-th subproblem.

       S      (output) DOUBLE PRECISION array, dimension ( N ) if
              ICOMPQ = 1, and dimension 1 if ICOMPQ = 0. If ICOMPQ = 1 and the
              I-th subproblem is not square, on exit, S( I ) contains  the  S-
              value  of  a  Givens rotation related to the right null space of
              the I-th subproblem.

       WORK   (workspace) DOUBLE PRECISION array, dimension
              (6 * N + (SMLSIZ + 1)*(SMLSIZ + 1)).

       IWORK  (workspace) INTEGER array.
              Dimension must be at least (7 * N).

       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

