!>
!> DGSVJ1 is called from DGESVJ as a pre-processor and that is its main
!> purpose. It applies Jacobi rotations in the same way as DGESVJ does, but
!> it targets only particular pivots and it does not check convergence
!> (stopping criterion). Few tuning parameters (marked by [TP]) are
!> available for the implementer.
!>
!> Further Details
!> ~~~~~~~~~~~~~~~
!> DGSVJ1 applies few sweeps of Jacobi rotations in the column space of
!> the input M-by-N matrix A. The pivot pairs are taken from the (1,2)
!> off-diagonal block in the corresponding N-by-N Gram matrix A^T * A. The
!> block-entries (tiles) of the (1,2) off-diagonal block are marked by the
!> [x]'s in the following scheme:
!>
!>    | *  *  * [x] [x] [x]|
!>    | *  *  * [x] [x] [x]|    Row-cycling in the nblr-by-nblc [x] blocks.
!>    | *  *  * [x] [x] [x]|    Row-cyclic pivoting inside each [x] block.
!>    |[x] [x] [x] *  *  * |
!>    |[x] [x] [x] *  *  * |
!>    |[x] [x] [x] *  *  * |
!>
!> In terms of the columns of A, the first N1 columns are rotated 'against'
!> the remaining N-N1 columns, trying to increase the angle between the
!> corresponding subspaces. The off-diagonal block is N1-by(N-N1) and it is
!> tiled using quadratic tiles of side KBL. Here, KBL is a tuning parameter.
!> The number of sweeps is given in NSWEEP and the orthogonality threshold
!> is given in TOL.
!> 

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.
!> 

M

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

N

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

N1

!>          N1 is INTEGER
!>          N1 specifies the 2 x 2 block partition, the first N1 columns are
!>          rotated 'against' the remaining N-N1 columns of A.
!> 

A

!>          A is DOUBLE PRECISION array, dimension (LDA,N)
!>          On entry, M-by-N matrix A, such that A*diag(D) represents
!>          the input matrix.
!>          On exit,
!>          A_onexit * 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 N1, D, TOL and NSWEEP.)
!> 

LDA

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

D

!>          D is DOUBLE PRECISION array, dimension (N)
!>          The array D accumulates the scaling factors from the fast 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 N1, A, TOL and NSWEEP.)
!> 

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 onexit*diag(D_onexit).
!> 

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.
!> 

V

!>          V is DOUBLE PRECISION 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.
!> 

LDV

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

EPS

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

SFMIN

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

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 DABS(COS(angle(A(:,p),A(:,q)))) > TOL.
!> 

NSWEEP

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

WORK

!>          WORK is DOUBLE PRECISION array, dimension (LWORK)
!> 

LWORK

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

INFO

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

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Zlatko Drmac (Zagreb, Croatia) and Kresimir Veselic (Hagen, Germany)