SGSVJ0 is called from SGESVJ as a pre-processor and that is its main


 purpose. It applies Jacobi rotations in the same way as SGESVJ does, but


 it does not check convergence (stopping criterion). Few tuning


 parameters (marked by [TP]) are available for the implementer.

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.

A

          A is REAL 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 D, TOL and NSWEEP.)

LDA

          LDA is INTEGER


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

D

          D is REAL 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 A, TOL and NSWEEP.)

SVA

          SVA is REAL 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 REAL 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 REAL


          EPS = SLAMCH('Epsilon')

SFMIN

          SFMIN is REAL


          SFMIN = SLAMCH('Safe Minimum')

TOL

          TOL is REAL


          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.

NSWEEP

          NSWEEP is INTEGER


          NSWEEP is the number of sweeps of Jacobi rotations to be


          performed.

WORK

          WORK is REAL 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

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

SGSVJ0 is used just to enable SGESVJ to call a simplified version of itself to work on a submatrix of the original matrix.

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

Please report all bugs and send interesting test examples and comments to drmac@math.hr. Thank you.