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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 computes 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 singular 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 bottom 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
         singular 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 components of
         the deflation-adjusted updating row vector for subproblems
         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
         permutations 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

  Further Details
  ===============

  Based on contributions by
     Ming Gu and Huan Ren, Computer Science Division, University of
     California at Berkeley, USA

