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## dlasd0()

subroutine dlasd0 | ( | integer | n,
|  | integer | sqre,
|  | double precision, dimension( * ) | d,
|  | double precision, dimension( * ) | e,
|  | double precision, dimension( ldu, * ) | u,
|  | integer | ldu,
|  | double precision, dimension( ldvt, * ) | vt,
|  | integer | ldvt,
|  | integer | smlsiz,
|  | integer, dimension( * ) | iwork,
|  | double precision, dimension( * ) | work,
|  | integer | info )

DLASD0 computes the singular values of a real upper bidiagonal n-by-m matrix B with diagonal d and off-diagonal e. Used by sbdsdc.

Download DLASD0 + dependencies [TGZ] [ZIP] [TXT]

Purpose:

      !>
      !> Using a divide and conquer approach, DLASD0 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 orthogonal matrices U and VT such that
      !> B = U * S * VT. The singular values S are overwritten on D.
      !>
      !> A related subroutine, DLASDA, computes only the singular values,
      !> and optionally, the singular vectors in compact form.
      !>

Parameters

  [in]

  N

      !>          N is INTEGER
      !>         On entry, the row dimension of the upper bidiagonal matrix.
      !>         This is also the dimension of the main diagonal array D.
      !>

  [in]

  SQRE

      !>          SQRE is 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;
      !>

  [in,out]

  D

      !>          D is 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.
      !>

  [in,out]

  E

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

  [in,out]

  U

      !>          U is DOUBLE PRECISION array, dimension (LDU, N)
      !>         On exit, U contains the left singular vectors,
      !>          if U passed in as (N, N) Identity.
      !>

  [in]

  LDU

      !>          LDU is INTEGER
      !>         On entry, leading dimension of U.
      !>

  [in,out]

  VT

      !>          VT is DOUBLE PRECISION array, dimension (LDVT, M)
      !>         On exit, VT**T contains the right singular vectors,
      !>          if VT passed in as (M, M) Identity.
      !>

  [in]

  LDVT

      !>          LDVT is INTEGER
      !>         On entry, leading dimension of VT.
      !>

  [in]

  SMLSIZ

      !>          SMLSIZ is INTEGER
      !>         On entry, maximum size of the subproblems at the
      !>         bottom of the computation tree.
      !>

  [out]

  IWORK

      !>          IWORK is INTEGER array, dimension (8*N)
      !>

  [out]

  WORK

      !>          WORK is DOUBLE PRECISION array, dimension (3*M**2+2*M)
      !>

  [out]

  INFO

      !>          INFO is INTEGER
      !>          = 0:  successful exit.
      !>          < 0:  if INFO = -i, the i-th argument had an illegal value.
      !>          > 0:  if INFO = 1, a singular value did not converge
      !>

Author
  Univ. of Tennessee
  Univ. of California Berkeley
  Univ. of Colorado Denver
  NAG Ltd.

Contributors:
  Ming Gu and Huan Ren, Computer Science Division, University of California at Berkeley, USA