OpenBLAS/lapack-netlib/SRC/cgsvj1.f

*> \brief \b CGSVJ1 pre-processor for the routine cgesvj, applies Jacobi rotations targeting only particular pivots.
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at
*            http://www.netlib.org/lapack/explore-html/
*
*> \htmlonly
*> Download CGSVJ1 + dependencies
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*> [TGZ]</a>
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*> [ZIP]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/cgsvj1.f">
*> [TXT]</a>
*> \endhtmlonly
*
*  Definition:
*  ===========
*
*       SUBROUTINE CGSVJ1( JOBV, M, N, N1, A, LDA, D, SVA, MV, V, LDV,
*                          EPS, SFMIN, TOL, NSWEEP, WORK, LWORK, INFO )
*
*       .. Scalar Arguments ..
*       REAL               EPS, SFMIN, TOL
*       INTEGER            INFO, LDA, LDV, LWORK, M, MV, N, N1, NSWEEP
*       CHARACTER*1        JOBV
*       ..
*       .. Array Arguments ..
*       COMPLEX            A( LDA, * ), D( N ), V( LDV, * ), WORK( LWORK )
*       REAL               SVA( N )
*       ..
*
*
*> \par Purpose:
*  =============
*>
*> \verbatim
*>
*> CGSVJ1 is called from CGESVJ as a pre-processor and that is its main
*> purpose. It applies Jacobi rotations in the same way as CGESVJ 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
*> ~~~~~~~~~~~~~~~
*> CGSVJ1 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 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.
*> \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 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 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 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).
*> \endverbatim
*>
*> \param[in] MV
*> \verbatim
*>          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.
*> \endverbatim
*>
*> \param[in,out] V
*> \verbatim
*>          V is COMPLEX 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.
*> \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 REAL
*>          EPS = SLAMCH('Epsilon')
*> \endverbatim
*>
*> \param[in] SFMIN
*> \verbatim
*>          SFMIN is REAL
*>          SFMIN = SLAMCH('Safe Minimum')
*> \endverbatim
*>
*> \param[in] TOL
*> \verbatim
*>          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.
*> \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 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 complexOTHERcomputational
*
*> \par Contributor:
*  ==================
*>
*> Zlatko Drmac (Zagreb, Croatia)
*
*  =====================================================================
      SUBROUTINE CGSVJ1( 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..--
*
*     .. Scalar Arguments ..
      REAL               EPS, SFMIN, TOL
      INTEGER            INFO, LDA, LDV, LWORK, M, MV, N, N1, NSWEEP
      CHARACTER*1        JOBV
*     ..
*     .. Array Arguments ..
      COMPLEX            A( LDA, * ), D( N ), V( LDV, * ), WORK( LWORK )
      REAL               SVA( N )
*     ..
*
*  =====================================================================
*
*     .. Local Parameters ..
      REAL               ZERO, HALF, ONE
      PARAMETER          ( ZERO = 0.0E0, HALF = 0.5E0, ONE = 1.0E0)
*     ..
*     .. Local Scalars ..
      COMPLEX            AAPQ, OMPQ
      REAL               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, MAX, CONJG, REAL, MIN, SIGN, SQRT
*     ..
*     .. External Functions ..
      REAL               SCNRM2
      COMPLEX            CDOTC
      INTEGER            ISAMAX
      LOGICAL            LSAME
      EXTERNAL           ISAMAX, LSAME, CDOTC, SCNRM2
*     ..
*     .. External Subroutines ..
*     .. from BLAS
      EXTERNAL           CCOPY, CROT, CSWAP, CAXPY
*     .. from LAPACK
      EXTERNAL           CLASCL, CLASSQ, 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( 'CGSVJ1', -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( REAL( 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 CGESVJ is used as a computational routine in the preconditioned
*     Jacobi SVD algorithm CGEJSV.
*
*
*     | *   *   * [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 = ( CDOTC( M, A( 1, p ), 1,
     $                                  A( 1, q ), 1 ) / AAQQ ) / AAPP
                              ELSE
                                 CALL CCOPY( M, A( 1, p ), 1,
     $                                       WORK, 1 )
                                 CALL CLASCL( 'G', 0, 0, AAPP,
     $                                        ONE, M, 1,
     $                                        WORK, LDA, IERR )
                                 AAPQ = CDOTC( M, WORK, 1,
     $                                  A( 1, q ), 1 ) / AAQQ
                              END IF
                           ELSE
                              IF( AAPP.GE.AAQQ ) THEN
                                 ROTOK = AAPP.LE.( AAQQ / SMALL )
                              ELSE
                                 ROTOK = AAQQ.LE.( AAPP / SMALL )
                              END IF
                              IF( AAPP.GT.( SMALL / AAQQ ) ) THEN
                                 AAPQ = ( CDOTC( M, A( 1, p ), 1,
     $                                 A( 1, q ), 1 ) / MAX(AAQQ,AAPP) )
     $                                               / MIN(AAQQ,AAPP)
                              ELSE
                                 CALL CCOPY( M, A( 1, q ), 1,
     $                                       WORK, 1 )
                                 CALL CLASCL( 'G', 0, 0, AAQQ,
     $                                        ONE, M, 1,
     $                                        WORK, LDA, IERR )
                                 AAPQ = CDOTC( 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 ...
*
                           IF( ABS( AAPQ1 ).GT.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
                                 IF( AAQQ.GT.AAPP0 )THETA = -THETA
*
                                 IF( ABS( THETA ).GT.BIGTHETA ) THEN
                                    T  = HALF / THETA
                                    CS = ONE
                                    CALL CROT( M, A(1,p), 1, A(1,q), 1,
     $                                          CS, CONJG(OMPQ)*T )
                                    IF( RSVEC ) THEN
                                        CALL CROT( 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 )
                                    IF( AAQQ.GT.AAPP0 )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 CROT( M, A(1,p), 1, A(1,q), 1,
     $                                          CS, CONJG(OMPQ)*SN )
                                    IF( RSVEC ) THEN
                                        CALL CROT( 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
                               IF( AAPP.GT.AAQQ ) THEN
                                    CALL CCOPY( M, A( 1, p ), 1,
     $                                          WORK, 1 )
                                    CALL CLASCL( 'G', 0, 0, AAPP, ONE,
     $                                           M, 1, WORK,LDA,
     $                                           IERR )
                                    CALL CLASCL( 'G', 0, 0, AAQQ, ONE,
     $                                           M, 1, A( 1, q ), LDA,
     $                                           IERR )
                                    CALL CAXPY( M, -AAPQ, WORK,
     $                                          1, A( 1, q ), 1 )
                                    CALL CLASCL( '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 CCOPY( M, A( 1, q ), 1,
     $                                          WORK, 1 )
                                    CALL CLASCL( 'G', 0, 0, AAQQ, ONE,
     $                                           M, 1, WORK,LDA,
     $                                           IERR )
                                    CALL CLASCL( 'G', 0, 0, AAPP, ONE,
     $                                           M, 1, A( 1, p ), LDA,
     $                                           IERR )
                                    CALL CAXPY( M, -CONJG(AAPQ),
     $                                   WORK, 1, A( 1, p ), 1 )
                                    CALL CLASCL( '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)
                              IF( ( SVA( q ) / AAQQ )**2.LE.ROOTEPS )
     $                            THEN
                                 IF( ( AAQQ.LT.ROOTBIG ) .AND.
     $                               ( AAQQ.GT.ROOTSFMIN ) ) THEN
                                    SVA( q ) = SCNRM2( M, A( 1, q ), 1)
                                  ELSE
                                    T = ZERO
                                    AAQQ = ONE
                                    CALL CLASSQ( M, A( 1, q ), 1, T,
     $                                           AAQQ )
                                    SVA( q ) = T*SQRT( AAQQ )
                                 END IF
                              END IF
                              IF( ( AAPP / AAPP0 )**2.LE.ROOTEPS ) THEN
                                 IF( ( AAPP.LT.ROOTBIG ) .AND.
     $                               ( AAPP.GT.ROOTSFMIN ) ) THEN
                                    AAPP = SCNRM2( M, A( 1, p ), 1 )
                                 ELSE
                                    T = ZERO
                                    AAPP = ONE
                                    CALL CLASSQ( 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
*
                        IF( ( i.LE.SWBAND ) .AND. ( IJBLSK.GE.BLSKIP ) )
     $                      THEN
                           SVA( p ) = AAPP
                           NOTROT = 0
                           GO TO 2011
                        END IF
                        IF( ( i.LE.SWBAND ) .AND.
     $                      ( PSKIPPED.GT.ROWSKIP ) ) THEN
                           AAPP = -AAPP
                           NOTROT = 0
                           GO TO 2203
                        END IF
*
 2200                CONTINUE
*        end of the q-loop
 2203                CONTINUE
*
                     SVA( p ) = AAPP
*
                  ELSE
*
                     IF( AAPP.EQ.ZERO )NOTROT = NOTROT +
     $                   MIN( jgl+KBL-1, N ) - jgl + 1
                     IF( AAPP.LT.ZERO )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)
         IF( ( SVA( N ).LT.ROOTBIG ) .AND. ( SVA( N ).GT.ROOTSFMIN ) )
     $       THEN
            SVA( N ) = SCNRM2( M, A( 1, N ), 1 )
         ELSE
            T = ZERO
            AAPP = ONE
            CALL CLASSQ( M, A( 1, N ), 1, T, AAPP )
            SVA( N ) = T*SQRT( AAPP )
         END IF
*
*     Additional steering devices
*
         IF( ( i.LT.SWBAND ) .AND. ( ( MXAAPQ.LE.ROOTTOL ) .OR.
     $       ( ISWROT.LE.N ) ) )SWBAND = i
*
         IF( ( i.GT.SWBAND+1 ) .AND. ( MXAAPQ.LT.SQRT( REAL( N ) )*
     $       TOL ) .AND. ( REAL( N )*MXAAPQ*MXSINJ.LT.TOL ) ) THEN
            GO TO 1994
         END IF
*
         IF( NOTROT.GE.EMPTSW )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 = ISAMAX( N-p+1, SVA( p ), 1 ) + p - 1
         IF( p.NE.q ) THEN
            TEMP1 = SVA( p )
            SVA( p ) = SVA( q )
            SVA( q ) = TEMP1
            AAPQ = D( p )
            D( p ) = D( q )
            D( q ) = AAPQ
            CALL CSWAP( M, A( 1, p ), 1, A( 1, q ), 1 )
            IF( RSVEC )CALL CSWAP( MVL, V( 1, p ), 1, V( 1, q ), 1 )
         END IF
 5991 CONTINUE
*
*
      RETURN
*     ..
*     .. END OF CGSVJ1
*     ..
      END