zgsvj1.f

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*> \brief \b ZGSVJ1 pre-processor for the routine zgesvj, applies Jacobi rotations targeting only particular pivots.
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at
*            http://www.netlib.org/lapack/explore-html/
*
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*> \endhtmlonly
*
*  Definition:
*  ===========
*
*       SUBROUTINE ZGSVJ1( JOBV, M, N, N1, A, LDA, D, SVA, MV, V, LDV,
*                          EPS, SFMIN, TOL, NSWEEP, WORK, LWORK, INFO )
*
*       .. Scalar Arguments ..
*       DOUBLE PRECISION   EPS, SFMIN, TOL
*       INTEGER            INFO, LDA, LDV, LWORK, M, MV, N, N1, NSWEEP
*       CHARACTER*1        JOBV
*       ..
*       .. Array Arguments ..
*       COMPLEX*16         A( LDA, * ), D( N ), V( LDV, * ), WORK( LWORK )
*       DOUBLE PRECISION   SVA( N )
*       ..
*
*
*> \par Purpose:
*  =============
*>
*> \verbatim
*>
*> ZGSVJ1 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 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
*> ~~~~~~~~~~~~~~~
*> ZGSVJ1 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.
*> \endverbatim
*
*  Arguments:
*  ==========
*
*> \param[in] JOBV
*> \verbatim
*>          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.
*> \endverbatim
*>
*> \param[in] M
*> \verbatim
*>          M is INTEGER
*>          The number of rows of the input matrix A.  M >= 0.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*>          N is INTEGER
*>          The number of columns of the input matrix A.
*>          M >= N >= 0.
*> \endverbatim
*>
*> \param[in] N1
*> \verbatim
*>          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.
*> \endverbatim
*>
*> \param[in,out] A
*> \verbatim
*>          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 * 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.)
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*>          LDA is INTEGER
*>          The leading dimension of the array A.  LDA >= max(1,M).
*> \endverbatim
*>
*> \param[in,out] D
*> \verbatim
*>          D is COMPLEX*16 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.)
*> \endverbatim
*>
*> \param[in,out] SVA
*> \verbatim
*>          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).
*> \endverbatim
*>
*> \param[in] MV
*> \verbatim
*>          MV is INTEGER
*>          If JOBV = 'A', then MV rows of V are post-multipled by a
*>                           sequence of Jacobi rotations.
*>          If JOBV = 'N',   then MV is not referenced.
*> \endverbatim
*>
*> \param[in,out] V
*> \verbatim
*>          V is COMPLEX*16 array, dimension (LDV,N)
*>          If JOBV = 'V' then N rows of V are post-multipled by a
*>                           sequence of Jacobi rotations.
*>          If JOBV = 'A' then MV rows of V are post-multipled by a
*>                           sequence of Jacobi rotations.
*>          If JOBV = 'N',   then V is not referenced.
*> \endverbatim
*>
*> \param[in] LDV
*> \verbatim
*>          LDV is INTEGER
*>          The leading dimension of the array V,  LDV >= 1.
*>          If JOBV = 'V', LDV >= N.
*>          If JOBV = 'A', LDV >= MV.
*> \endverbatim
*>
*> \param[in] EPS
*> \verbatim
*>          EPS is DOUBLE PRECISION
*>          EPS = DLAMCH('Epsilon')
*> \endverbatim
*>
*> \param[in] SFMIN
*> \verbatim
*>          SFMIN is DOUBLE PRECISION
*>          SFMIN = DLAMCH('Safe Minimum')
*> \endverbatim
*>
*> \param[in] TOL
*> \verbatim
*>          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.
*> \endverbatim
*>
*> \param[in] NSWEEP
*> \verbatim
*>          NSWEEP is INTEGER
*>          NSWEEP is the number of sweeps of Jacobi rotations to be
*>          performed.
*> \endverbatim
*>
*> \param[out] WORK
*> \verbatim
*>          WORK is COMPLEX*16 array, dimension (LWORK)
*> \endverbatim
*>
*> \param[in] LWORK
*> \verbatim
*>          LWORK is INTEGER
*>          LWORK is the dimension of WORK. LWORK >= M.
*> \endverbatim
*>
*> \param[out] INFO
*> \verbatim
*>          INFO is INTEGER
*>          = 0:  successful exit.
*>          < 0:  if INFO = -i, then the i-th argument had an illegal value
*> \endverbatim
*
*  Authors:
*  ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \ingroup complex16OTHERcomputational
*
*> \par Contributor:
*  ==================
*>
*> Zlatko Drmac (Zagreb, Croatia)
*
*  =====================================================================
      SUBROUTINE zgsvj1( JOBV, M, N, N1, A, LDA, D, SVA, MV, V, LDV,
     $                   EPS, SFMIN, TOL, NSWEEP, WORK, LWORK, INFO )
*
*  -- LAPACK computational routine --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*
      IMPLICIT NONE
*     .. Scalar Arguments ..
      DOUBLE PRECISION   EPS, SFMIN, TOL
      INTEGER            INFO, LDA, LDV, LWORK, M, MV, N, N1, NSWEEP
      CHARACTER*1        JOBV
*     ..
*     .. Array Arguments ..
      COMPLEX*16         A( LDA, * ), D( N ), V( LDV, * ), WORK( LWORK )
      DOUBLE PRECISION   SVA( N )
*     ..
*
*  =====================================================================
*
*     .. Local Parameters ..
      DOUBLE PRECISION   ZERO, HALF, ONE
      parameter( zero = 0.0d0, half = 0.5d0, one = 1.0d0)
*     ..
*     .. Local Scalars ..
      COMPLEX*16         AAPQ, OMPQ
      DOUBLE PRECISION   AAPP, AAPP0, AAPQ1, AAQQ, APOAQ, AQOAP, BIG,
     $                   bigtheta, cs, mxaapq, mxsinj, rootbig,
     $                   rooteps, rootsfmin, roottol, small, sn, t,
     $                   temp1, theta, thsign
      INTEGER            BLSKIP, EMPTSW, i, ibr, igl, IERR, IJBLSK,
     $                   iswrot, jbc, jgl, kbl, mvl, notrot, nblc, nblr,
     $                   p, pskipped, q, rowskip, swband
      LOGICAL            APPLV, ROTOK, RSVEC
*     ..
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          abs, conjg, max, dble, min, sign, sqrt
*     ..
*     .. External Functions ..
      DOUBLE PRECISION   DZNRM2
      COMPLEX*16         ZDOTC
      INTEGER            IDAMAX
      LOGICAL            LSAME
      EXTERNAL           idamax, lsame, zdotc, dznrm2
*     ..
*     .. External Subroutines ..
*     .. from BLAS
      EXTERNAL           zcopy, zrot, zswap, zaxpy
*     .. from LAPACK
      EXTERNAL           zlascl, zlassq, xerbla
*     ..
*     .. Executable Statements ..
*
*     Test the input parameters.
*
      applv = lsame( jobv, 'A' )
      rsvec = lsame( jobv, 'V' )
      IF( .NOT.( rsvec .OR. applv .OR. lsame( jobv, 'N' ) ) ) THEN
         info = -1
      ELSE IF( m.LT.0 ) THEN
         info = -2
      ELSE IF( ( n.LT.0 ) .OR. ( n.GT.m ) ) THEN
         info = -3
      ELSE IF( n1.LT.0 ) THEN
         info = -4
      ELSE IF( lda.LT.m ) THEN
         info = -6
      ELSE IF( ( rsvec.OR.applv ) .AND. ( mv.LT.0 ) ) THEN
         info = -9
      ELSE IF( ( rsvec.AND.( ldv.LT.n ) ).OR.
     $         ( applv.AND.( ldv.LT.mv ) )  ) THEN
         info = -11
      ELSE IF( tol.LE.eps ) THEN
         info = -14
      ELSE IF( nsweep.LT.0 ) THEN
         info = -15
      ELSE IF( lwork.LT.m ) THEN
         info = -17
      ELSE
         info = 0
      END IF
*
*     #:(
      IF( info.NE.0 ) THEN
         CALL xerbla( 'ZGSVJ1', -info )
         RETURN
      END IF
*
      IF( rsvec ) THEN
         mvl = n
      ELSE IF( applv ) THEN
         mvl = mv
      END IF
      rsvec = rsvec .OR. applv
 
      rooteps = sqrt( eps )
      rootsfmin = sqrt( sfmin )
      small = sfmin / eps
      big = one / sfmin
      rootbig = one / rootsfmin
*     LARGE = BIG / SQRT( DBLE( M*N ) )
      bigtheta = one / rooteps
      roottol = sqrt( tol )
*
*     .. Initialize the right singular vector matrix ..
*
*     RSVEC = LSAME( JOBV, 'Y' )
*
      emptsw = n1*( n-n1 )
      notrot = 0
*
*     .. Row-cyclic pivot strategy with de Rijk's pivoting ..
*
      kbl = min( 8, n )
      nblr = n1 / kbl
      IF( ( nblr*kbl ).NE.n1 )nblr = nblr + 1
 
*     .. the tiling is nblr-by-nblc [tiles]
 
      nblc = ( n-n1 ) / kbl
      IF( ( nblc*kbl ).NE.( n-n1 ) )nblc = nblc + 1
      blskip = ( kbl**2 ) + 1
*[TP] BLKSKIP is a tuning parameter that depends on SWBAND and KBL.
 
      rowskip = min( 5, kbl )
*[TP] ROWSKIP is a tuning parameter.
      swband = 0
*[TP] SWBAND is a tuning parameter. It is meaningful and effective
*     if ZGESVJ is used as a computational routine in the preconditioned
*     Jacobi SVD algorithm ZGEJSV.
*
*
*     | *   *   * [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] *   *   * |
*
*
      DO 1993 i = 1, nsweep
*
*     .. go go go ...
*
         mxaapq = zero
         mxsinj = zero
         iswrot = 0
*
         notrot = 0
         pskipped = 0
*
*     Each sweep is unrolled using KBL-by-KBL tiles over the pivot pairs
*     1 <= p < q <= N. This is the first step toward a blocked implementation
*     of the rotations. New implementation, based on block transformations,
*     is under development.
*
         DO 2000 ibr = 1, nblr
*
            igl = ( ibr-1 )*kbl + 1
*
 
*
* ... go to the off diagonal blocks
*
            igl = ( ibr-1 )*kbl + 1
*
*            DO 2010 jbc = ibr + 1, NBL
            DO 2010 jbc = 1, nblc
*
               jgl = ( jbc-1 )*kbl + n1 + 1
*
*        doing the block at ( ibr, jbc )
*
               ijblsk = 0
               DO 2100 p = igl, min( igl+kbl-1, n1 )
*
                  aapp = sva( p )
                  IF( aapp.GT.zero ) THEN
*
                     pskipped = 0
*
                     DO 2200 q = jgl, min( jgl+kbl-1, n )
*
                        aaqq = sva( q )
                        IF( aaqq.GT.zero ) THEN
                           aapp0 = aapp
*
*     .. M x 2 Jacobi SVD ..
*
*        Safe Gram matrix computation
*
                           IF( aaqq.GE.one ) THEN
                              IF( aapp.GE.aaqq ) THEN
                                 rotok = ( small*aapp ).LE.aaqq
                              ELSE
                                 rotok = ( small*aaqq ).LE.aapp
                              END IF
                              IF( aapp.LT.( big / aaqq ) ) THEN
                                 aapq = ( zdotc( m, a( 1, p ), 1,
     $                                  a( 1, q ), 1 ) / aaqq ) / aapp
                              ELSE
                                 CALL zcopy( m, a( 1, p ), 1,
     $                                       work, 1 )
                                 CALL zlascl( 'g', 0, 0, AAPP,
     $                                        ONE, M, 1,
     $                                        WORK, LDA, IERR )
                                 AAPQ = ZDOTC( M, WORK, 1,
     $                                  A( 1, q ), 1 ) / AAQQ
                              END IF
                           ELSE
.GE.                              IF( AAPPAAQQ ) THEN
.LE.                                 ROTOK = AAPP( AAQQ / SMALL )
                              ELSE
.LE.                                 ROTOK = AAQQ( AAPP / SMALL )
                              END IF
.GT.                              IF( AAPP( SMALL / AAQQ ) ) THEN
                                 AAPQ = ( ZDOTC( M, A( 1, p ), 1,
     $                                 A( 1, q ), 1 ) / MAX(AAQQ,AAPP) )
     $                                               / MIN(AAQQ,AAPP)
                              ELSE
                                 CALL ZCOPY( M, A( 1, q ), 1,
     $                                       WORK, 1 )
                                 CALL ZLASCL( 'g', 0, 0, AAQQ,
     $                                        ONE, M, 1,
     $                                        WORK, LDA, IERR )
                                 AAPQ = ZDOTC( M, A( 1, p ), 1,
     $                                  WORK, 1 ) / AAPP
                              END IF
                           END IF
*
*                           AAPQ = AAPQ * CONJG(CWORK(p))*CWORK(q)
                           AAPQ1  = -ABS(AAPQ)
                           MXAAPQ = MAX( MXAAPQ, -AAPQ1 )
*
*        TO rotate or NOT to rotate, THAT is the question ...
*
.GT.                           IF( ABS( AAPQ1 )TOL ) THEN
                              OMPQ = AAPQ / ABS(AAPQ)
                              NOTROT = 0
*[RTD]      ROTATED  = ROTATED + 1
                              PSKIPPED = 0
                              ISWROT = ISWROT + 1
*
                              IF( ROTOK ) THEN
*
                                 AQOAP = AAQQ / AAPP
                                 APOAQ = AAPP / AAQQ
                                 THETA = -HALF*ABS( AQOAP-APOAQ )/ AAPQ1
.GT.                                 IF( AAQQAAPP0 )THETA = -THETA
*
.GT.                                 IF( ABS( THETA )BIGTHETA ) THEN
                                    T  = HALF / THETA
                                    CS = ONE
                                    CALL ZROT( M, A(1,p), 1, A(1,q), 1,
     $                                          CS, CONJG(OMPQ)*T )
                                    IF( RSVEC ) THEN
                                        CALL ZROT( MVL, V(1,p), 1,
     $                                  V(1,q), 1, CS, CONJG(OMPQ)*T )
                                    END IF
                                    SVA( q ) = AAQQ*SQRT( MAX( ZERO,
     $                                         ONE+T*APOAQ*AAPQ1 ) )
                                    AAPP = AAPP*SQRT( MAX( ZERO,
     $                                     ONE-T*AQOAP*AAPQ1 ) )
                                    MXSINJ = MAX( MXSINJ, ABS( T ) )
                                 ELSE
*
*                 .. choose correct signum for THETA and rotate
*
                                    THSIGN = -SIGN( ONE, AAPQ1 )
.GT.                                    IF( AAQQAAPP0 )THSIGN = -THSIGN
                                    T = ONE / ( THETA+THSIGN*
     $                                  SQRT( ONE+THETA*THETA ) )
                                    CS = SQRT( ONE / ( ONE+T*T ) )
                                    SN = T*CS
                                    MXSINJ = MAX( MXSINJ, ABS( SN ) )
                                    SVA( q ) = AAQQ*SQRT( MAX( ZERO,
     $                                         ONE+T*APOAQ*AAPQ1 ) )
                                    AAPP = AAPP*SQRT( MAX( ZERO,
     $                                         ONE-T*AQOAP*AAPQ1 ) )
*
                                    CALL ZROT( M, A(1,p), 1, A(1,q), 1,
     $                                          CS, CONJG(OMPQ)*SN )
                                    IF( RSVEC ) THEN
                                        CALL ZROT( MVL, V(1,p), 1,
     $                                  V(1,q), 1, CS, CONJG(OMPQ)*SN )
                                    END IF
                                 END IF
                                 D(p) = -D(q) * OMPQ
*
                              ELSE
*              .. have to use modified Gram-Schmidt like transformation
.GT.                               IF( AAPPAAQQ ) THEN
                                    CALL ZCOPY( M, A( 1, p ), 1,
     $                                          WORK, 1 )
                                    CALL ZLASCL( 'g', 0, 0, AAPP, ONE,
     $                                           M, 1, WORK,LDA,
     $                                           IERR )
                                    CALL ZLASCL( 'g', 0, 0, AAQQ, ONE,
     $                                           M, 1, A( 1, q ), LDA,
     $                                           IERR )
                                    CALL ZAXPY( M, -AAPQ, WORK,
     $                                          1, A( 1, q ), 1 )
                                    CALL ZLASCL( 'g', 0, 0, ONE, AAQQ,
     $                                           M, 1, A( 1, q ), LDA,
     $                                           IERR )
                                    SVA( q ) = AAQQ*SQRT( MAX( ZERO,
     $                                         ONE-AAPQ1*AAPQ1 ) )
                                    MXSINJ = MAX( MXSINJ, SFMIN )
                               ELSE
                                   CALL ZCOPY( M, A( 1, q ), 1,
     $                                          WORK, 1 )
                                    CALL ZLASCL( 'g', 0, 0, AAQQ, ONE,
     $                                           M, 1, WORK,LDA,
     $                                           IERR )
                                    CALL ZLASCL( 'g', 0, 0, AAPP, ONE,
     $                                           M, 1, A( 1, p ), LDA,
     $                                           IERR )
                                    CALL ZAXPY( M, -CONJG(AAPQ),
     $                                   WORK, 1, A( 1, p ), 1 )
                                    CALL ZLASCL( 'g', 0, 0, ONE, AAPP,
     $                                           M, 1, A( 1, p ), LDA,
     $                                           IERR )
                                    SVA( p ) = AAPP*SQRT( MAX( ZERO,
     $                                         ONE-AAPQ1*AAPQ1 ) )
                                    MXSINJ = MAX( MXSINJ, SFMIN )
                               END IF
                              END IF
*           END IF ROTOK THEN ... ELSE
*
*           In the case of cancellation in updating SVA(q), SVA(p)
*           .. recompute SVA(q), SVA(p)
.LE.                              IF( ( SVA( q ) / AAQQ )**2ROOTEPS )
     $                            THEN
.LT..AND.                                 IF( ( AAQQROOTBIG ) 
.GT.     $                               ( AAQQROOTSFMIN ) ) THEN
                                    SVA( q ) = DZNRM2( M, A( 1, q ), 1)
                                  ELSE
                                    T = ZERO
                                    AAQQ = ONE
                                    CALL ZLASSQ( M, A( 1, q ), 1, T,
     $                                           AAQQ )
                                    SVA( q ) = T*SQRT( AAQQ )
                                 END IF
                              END IF
.LE.                              IF( ( AAPP / AAPP0 )**2ROOTEPS ) THEN
.LT..AND.                                 IF( ( AAPPROOTBIG ) 
.GT.     $                               ( AAPPROOTSFMIN ) ) THEN
                                    AAPP = DZNRM2( M, A( 1, p ), 1 )
                                 ELSE
                                    T = ZERO
                                    AAPP = ONE
                                    CALL ZLASSQ( M, A( 1, p ), 1, T,
     $                                           AAPP )
                                    AAPP = T*SQRT( AAPP )
                                 END IF
                                 SVA( p ) = AAPP
                              END IF
*              end of OK rotation
                           ELSE
                              NOTROT = NOTROT + 1
*[RTD]      SKIPPED  = SKIPPED  + 1
                              PSKIPPED = PSKIPPED + 1
                              IJBLSK = IJBLSK + 1
                           END IF
                        ELSE
                           NOTROT = NOTROT + 1
                           PSKIPPED = PSKIPPED + 1
                           IJBLSK = IJBLSK + 1
                        END IF
*
.LE..AND..GE.                        IF( ( iSWBAND )  ( IJBLSKBLSKIP ) )
     $                      THEN
                           SVA( p ) = AAPP
                           NOTROT = 0
                           GO TO 2011
                        END IF
.LE..AND.                        IF( ( iSWBAND ) 
.GT.     $                      ( PSKIPPEDROWSKIP ) ) THEN
                           AAPP = -AAPP
                           NOTROT = 0
                           GO TO 2203
                        END IF
*
 2200                CONTINUE
*        end of the q-loop
 2203                CONTINUE
*
                     SVA( p ) = AAPP
*
                  ELSE
*
.EQ.                     IF( AAPPZERO )NOTROT = NOTROT +
     $                   MIN( jgl+KBL-1, N ) - jgl + 1
.LT.                     IF( AAPPZERO )NOTROT = 0
*
                  END IF
*
 2100          CONTINUE
*     end of the p-loop
 2010       CONTINUE
*     end of the jbc-loop
 2011       CONTINUE
*2011 bailed out of the jbc-loop
            DO 2012 p = igl, MIN( igl+KBL-1, N )
               SVA( p ) = ABS( SVA( p ) )
 2012       CONTINUE
***
 2000    CONTINUE
*2000 :: end of the ibr-loop
*
*     .. update SVA(N)
.LT..AND..GT.         IF( ( SVA( N )ROOTBIG )  ( SVA( N )ROOTSFMIN ) )
     $       THEN
            SVA( N ) = DZNRM2( M, A( 1, N ), 1 )
         ELSE
            T = ZERO
            AAPP = ONE
            CALL ZLASSQ( M, A( 1, N ), 1, T, AAPP )
            SVA( N ) = T*SQRT( AAPP )
         END IF
*
*     Additional steering devices
*
.LT..AND..LE..OR.         IF( ( iSWBAND )  ( ( MXAAPQROOTTOL ) 
.LE.     $       ( ISWROTN ) ) )SWBAND = i
*
.GT..AND..LT.         IF( ( iSWBAND+1 )  ( MXAAPQSQRT( DBLE( N ) )*
.AND..LT.     $       TOL )  ( DBLE( N )*MXAAPQ*MXSINJTOL ) ) THEN
            GO TO 1994
         END IF
*
.GE.         IF( NOTROTEMPTSW )GO TO 1994
*
 1993 CONTINUE
*     end i=1:NSWEEP loop
*
* #:( Reaching this point means that the procedure has not converged.
      INFO = NSWEEP - 1
      GO TO 1995
*
 1994 CONTINUE
* #:) Reaching this point means numerical convergence after the i-th
*     sweep.
*
      INFO = 0
* #:) INFO = 0 confirms successful iterations.
 1995 CONTINUE
*
*     Sort the vector SVA() of column norms.
      DO 5991 p = 1, N - 1
         q = IDAMAX( N-p+1, SVA( p ), 1 ) + p - 1
.NE.         IF( pq ) THEN
            TEMP1 = SVA( p )
            SVA( p ) = SVA( q )
            SVA( q ) = TEMP1
            AAPQ = D( p )
            D( p ) = D( q )
            D( q ) = AAPQ
            CALL ZSWAP( M, A( 1, p ), 1, A( 1, q ), 1 )
            IF( RSVEC )CALL ZSWAP( MVL, V( 1, p ), 1, V( 1, q ), 1 )
         END IF
 5991 CONTINUE
*
*
      RETURN
*     ..
*     .. END OF ZGSVJ1
*     ..
      END