SGSVJ0(3)      LAPACK routine of NEC Numeric Library Collection      SGSVJ0(3)



NAME
       SGSVJ0

SYNOPSIS
       SUBROUTINE SGSVJ0 (JOBV, M, N, A, LDA, D, SVA, MV, V, LDV, EPS, SFMIN,
           TOL, NSWEEP, WORK, LWORK, INFO)



PURPOSE
            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.




ARGUMENTS
           JOBV      (input)
                     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 postmulyiplying the N-by-N array V.
                           (See the description of V.)
                     = 'A': the product of the Jacobi rotations is accumulated
                            by postmulyiplying the MV-by-N array V.
                           (See the descriptions of MV and V.)
                     = 'N': the Jacobi rotations are not accumulated.

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

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

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

           D         (input/output)
                     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       (input/output)
                     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        (input)
                     MV is INTEGER
                     If JOBV .EQ. 'A', then MV rows of V are post-multipled by a
                                      sequence of Jacobi rotations.
                     If JOBV = 'N',   then MV is not referenced.

           V         (input/output)
                     V is REAL array, dimension (LDV,N)
                     If JOBV .EQ. 'V' then N rows of V are post-multipled by a
                                      sequence of Jacobi rotations.
                     If JOBV .EQ. 'A' then MV rows of V are post-multipled by a
                                      sequence of Jacobi rotations.
                     If JOBV = 'N',   then V is not referenced.

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

           EPS       (input)
                     EPS is REAL
                     EPS = SLAMCH('Epsilon')

           SFMIN     (input)
                     SFMIN is REAL
                     SFMIN = SLAMCH('Safe Minimum')

           TOL       (input)
                     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)))) .GT. TOL.

           NSWEEP    (input)
                     NSWEEP is INTEGER
                     NSWEEP is the number of sweeps of Jacobi rotations to be
                     performed.

           WORK      (output)
                     WORK is REAL array, dimension LWORK.

           LWORK     (input)
                     LWORK is INTEGER
                     LWORK is the dimension of WORK. LWORK .GE. M.

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






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



LAPACK routine                  31 October 2017                      SGSVJ0(3)