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## zgsvj0()

subroutine zgsvj0 | ( | character*1 | jobv,
|  | integer | m,
|  | integer | n,
|  | complex*16, dimension( lda, * ) | a,
|  | integer | lda,
|  | complex*16, dimension( n ) | d,
|  | double precision, dimension( n ) | sva,
|  | integer | mv,
|  | complex*16, dimension( ldv, * ) | v,
|  | integer | ldv,
|  | double precision | eps,
|  | double precision | sfmin,
|  | double precision | tol,
|  | integer | nsweep,
|  | complex*16, dimension( lwork ) | work,
|  | integer | lwork,
|  | integer | info )

ZGSVJ0 pre-processor for the routine zgesvj.

Download ZGSVJ0 + dependencies [TGZ] [ZIP] [TXT]

Purpose:

      !>
      !> ZGSVJ0 is called from ZGESVJ as a pre-processor and that is its main
      !> purpose. It applies Jacobi rotations in the same way as ZGESVJ does, but
      !> it does not check convergence (stopping criterion). Few tuning
      !> parameters (marked by [TP]) are available for the implementer.
      !>

Parameters

  [in]

  JOBV

      !>          JOBV is CHARACTER*1
      !>          Specifies whether the output from this procedure is used
      !>          to compute the matrix V:
      !>          = 'V': the product of the Jacobi rotations is accumulated
      !>                 by postmultiplying the N-by-N array V.
      !>                (See the description of V.)
      !>          = 'A': the product of the Jacobi rotations is accumulated
      !>                 by postmultiplying the MV-by-N array V.
      !>                (See the descriptions of MV and V.)
      !>          = 'N': the Jacobi rotations are not accumulated.
      !>

  [in]

  M

      !>          M is INTEGER
      !>          The number of rows of the input matrix A.  M >= 0.
      !>

  [in]

  N

      !>          N is INTEGER
      !>          The number of columns of the input matrix A.
      !>          M >= N >= 0.
      !>

  [in,out]

  A

      !>          A is COMPLEX*16 array, dimension (LDA,N)
      !>          On entry, M-by-N matrix A, such that A*diag(D) represents
      !>          the input matrix.
      !>          On exit,
      !>          A_onexit * diag(D_onexit) represents the input matrix A*diag(D)
      !>          post-multiplied by a sequence of Jacobi rotations, where the
      !>          rotation threshold and the total number of sweeps are given in
      !>          TOL and NSWEEP, respectively.
      !>          (See the descriptions of D, TOL and NSWEEP.)
      !>

  [in]

  LDA

      !>          LDA is INTEGER
      !>          The leading dimension of the array A.  LDA >= max(1,M).
      !>

  [in,out]

  D

      !>          D is COMPLEX*16 array, dimension (N)
      !>          The array D accumulates the scaling factors from the complex scaled
      !>          Jacobi rotations.
      !>          On entry, A*diag(D) represents the input matrix.
      !>          On exit, A_onexit*diag(D_onexit) represents the input matrix
      !>          post-multiplied by a sequence of Jacobi rotations, where the
      !>          rotation threshold and the total number of sweeps are given in
      !>          TOL and NSWEEP, respectively.
      !>          (See the descriptions of A, TOL and NSWEEP.)
      !>

  [in,out]

  SVA

      !>          SVA is DOUBLE PRECISION array, dimension (N)
      !>          On entry, SVA contains the Euclidean norms of the columns of
      !>          the matrix A*diag(D).
      !>          On exit, SVA contains the Euclidean norms of the columns of
      !>          the matrix A_onexit*diag(D_onexit).
      !>

  [in]

  MV

      !>          MV is INTEGER
      !>          If JOBV = 'A', then MV rows of V are post-multiplied by a
      !>                           sequence of Jacobi rotations.
      !>          If JOBV = 'N',   then MV is not referenced.
      !>

  [in,out]

  V

      !>          V is COMPLEX*16 array, dimension (LDV,N)
      !>          If JOBV = 'V' then N rows of V are post-multiplied by a
      !>                           sequence of Jacobi rotations.
      !>          If JOBV = 'A' then MV rows of V are post-multiplied by a
      !>                           sequence of Jacobi rotations.
      !>          If JOBV = 'N',   then V is not referenced.
      !>

  [in]

  LDV

      !>          LDV is INTEGER
      !>          The leading dimension of the array V,  LDV >= 1.
      !>          If JOBV = 'V', LDV >= N.
      !>          If JOBV = 'A', LDV >= MV.
      !>

  [in]

  EPS

      !>          EPS is DOUBLE PRECISION
      !>          EPS = DLAMCH('Epsilon')
      !>

  [in]

  SFMIN

      !>          SFMIN is DOUBLE PRECISION
      !>          SFMIN = DLAMCH('Safe Minimum')
      !>

  [in]

  TOL

      !>          TOL is DOUBLE PRECISION
      !>          TOL is the threshold for Jacobi rotations. For a pair
      !>          A(:,p), A(:,q) of pivot columns, the Jacobi rotation is
      !>          applied only if ABS(COS(angle(A(:,p),A(:,q)))) > TOL.
      !>

  [in]

  NSWEEP

      !>          NSWEEP is INTEGER
      !>          NSWEEP is the number of sweeps of Jacobi rotations to be
      !>          performed.
      !>

  [out]

  WORK

      !>          WORK is COMPLEX*16 array, dimension (LWORK)
      !>

  [in]

  LWORK

      !>          LWORK is INTEGER
      !>          LWORK is the dimension of WORK. LWORK >= M.
      !>

  [out]

  INFO

      !>          INFO is INTEGER
      !>          = 0:  successful exit.
      !>          < 0:  if INFO = -i, then the i-th argument had an illegal value
      !>

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

Further Details:
  ZGSVJ0 is used just to enable ZGESVJ to call a simplified version of itself to work on a submatrix of the original matrix.

Contributor: Zlatko Drmac (Zagreb, Croatia)

Bugs, Examples and Comments:
  Please report all bugs and send interesting test examples and comments to drmac.nosp@m.@mat.nosp@m.h.hr. Thank you.