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Diff for /rpl/lapack/lapack/dbdsqr.f between versions 1.13 and 1.19

version 1.13, 2016/08/27 15:34:19 version 1.19, 2023/08/07 08:38:47
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 *  *
 *  =========== DOCUMENTATION ===========  *  =========== DOCUMENTATION ===========
 *  *
 * Online html documentation available at   * Online html documentation available at
 *            http://www.netlib.org/lapack/explore-html/   *            http://www.netlib.org/lapack/explore-html/
 *  *
 *> \htmlonly  *> \htmlonly
 *> Download DBDSQR + dependencies   *> Download DBDSQR + dependencies
 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dbdsqr.f">   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dbdsqr.f">
 *> [TGZ]</a>   *> [TGZ]</a>
 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dbdsqr.f">   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dbdsqr.f">
 *> [ZIP]</a>   *> [ZIP]</a>
 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dbdsqr.f">   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dbdsqr.f">
 *> [TXT]</a>  *> [TXT]</a>
 *> \endhtmlonly   *> \endhtmlonly
 *  *
 *  Definition:  *  Definition:
 *  ===========  *  ===========
 *  *
 *       SUBROUTINE DBDSQR( UPLO, N, NCVT, NRU, NCC, D, E, VT, LDVT, U,  *       SUBROUTINE DBDSQR( UPLO, N, NCVT, NRU, NCC, D, E, VT, LDVT, U,
 *                          LDU, C, LDC, WORK, INFO )  *                          LDU, C, LDC, WORK, INFO )
 *   *
 *       .. Scalar Arguments ..  *       .. Scalar Arguments ..
 *       CHARACTER          UPLO  *       CHARACTER          UPLO
 *       INTEGER            INFO, LDC, LDU, LDVT, N, NCC, NCVT, NRU  *       INTEGER            INFO, LDC, LDU, LDVT, N, NCC, NCVT, NRU
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 *       DOUBLE PRECISION   C( LDC, * ), D( * ), E( * ), U( LDU, * ),  *       DOUBLE PRECISION   C( LDC, * ), D( * ), E( * ), U( LDU, * ),
 *      $                   VT( LDVT, * ), WORK( * )  *      $                   VT( LDVT, * ), WORK( * )
 *       ..  *       ..
 *    *
 *  *
 *> \par Purpose:  *> \par Purpose:
 *  =============  *  =============
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 *> left singular vectors from the singular value decomposition (SVD) of  *> left singular vectors from the singular value decomposition (SVD) of
 *> a real N-by-N (upper or lower) bidiagonal matrix B using the implicit  *> a real N-by-N (upper or lower) bidiagonal matrix B using the implicit
 *> zero-shift QR algorithm.  The SVD of B has the form  *> zero-shift QR algorithm.  The SVD of B has the form
 *>   *>
 *>    B = Q * S * P**T  *>    B = Q * S * P**T
 *>   *>
 *> where S is the diagonal matrix of singular values, Q is an orthogonal  *> where S is the diagonal matrix of singular values, Q is an orthogonal
 *> matrix of left singular vectors, and P is an orthogonal matrix of  *> matrix of left singular vectors, and P is an orthogonal matrix of
 *> right singular vectors.  If left singular vectors are requested, this  *> right singular vectors.  If left singular vectors are requested, this
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 *> \verbatim  *> \verbatim
 *>          E is DOUBLE PRECISION array, dimension (N-1)  *>          E is DOUBLE PRECISION array, dimension (N-1)
 *>          On entry, the N-1 offdiagonal elements of the bidiagonal  *>          On entry, the N-1 offdiagonal elements of the bidiagonal
 *>          matrix B.   *>          matrix B.
 *>          On exit, if INFO = 0, E is destroyed; if INFO > 0, D and E  *>          On exit, if INFO = 0, E is destroyed; if INFO > 0, D and E
 *>          will contain the diagonal and superdiagonal elements of a  *>          will contain the diagonal and superdiagonal elements of a
 *>          bidiagonal matrix orthogonally equivalent to the one given  *>          bidiagonal matrix orthogonally equivalent to the one given
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 *>  *>
 *> \param[out] WORK  *> \param[out] WORK
 *> \verbatim  *> \verbatim
 *>          WORK is DOUBLE PRECISION array, dimension (4*N)  *>          WORK is DOUBLE PRECISION array, dimension (4*(N-1))
 *> \endverbatim  *> \endverbatim
 *>  *>
 *> \param[out] INFO  *> \param[out] INFO
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 *>                = 1, a split was marked by a positive value in E  *>                = 1, a split was marked by a positive value in E
 *>                = 2, current block of Z not diagonalized after 30*N  *>                = 2, current block of Z not diagonalized after 30*N
 *>                     iterations (in inner while loop)  *>                     iterations (in inner while loop)
 *>                = 3, termination criterion of outer while loop not met   *>                = 3, termination criterion of outer while loop not met
 *>                     (program created more than N unreduced blocks)  *>                     (program created more than N unreduced blocks)
 *>             else NCVT = NRU = NCC = 0,  *>             else NCVT = NRU = NCC = 0,
 *>                   the algorithm did not converge; D and E contain the  *>                   the algorithm did not converge; D and E contain the
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 *>          algorithm through its inner loop. The algorithms stops  *>          algorithm through its inner loop. The algorithms stops
 *>          (and so fails to converge) if the number of passes  *>          (and so fails to converge) if the number of passes
 *>          through the inner loop exceeds MAXITR*N**2.  *>          through the inner loop exceeds MAXITR*N**2.
   *>
   *> \endverbatim
   *
   *> \par Note:
   *  ===========
   *>
   *> \verbatim
   *>  Bug report from Cezary Dendek.
   *>  On March 23rd 2017, the INTEGER variable MAXIT = MAXITR*N**2 is
   *>  removed since it can overflow pretty easily (for N larger or equal
   *>  than 18,919). We instead use MAXITDIVN = MAXITR*N.
 *> \endverbatim  *> \endverbatim
 *  *
 *  Authors:  *  Authors:
 *  ========  *  ========
 *  *
 *> \author Univ. of Tennessee   *> \author Univ. of Tennessee
 *> \author Univ. of California Berkeley   *> \author Univ. of California Berkeley
 *> \author Univ. of Colorado Denver   *> \author Univ. of Colorado Denver
 *> \author NAG Ltd.   *> \author NAG Ltd.
 *  
 *> \date November 2011  
 *  *
 *> \ingroup auxOTHERcomputational  *> \ingroup auxOTHERcomputational
 *  *
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       SUBROUTINE DBDSQR( UPLO, N, NCVT, NRU, NCC, D, E, VT, LDVT, U,        SUBROUTINE DBDSQR( UPLO, N, NCVT, NRU, NCC, D, E, VT, LDVT, U,
      $                   LDU, C, LDC, WORK, INFO )       $                   LDU, C, LDC, WORK, INFO )
 *  *
 *  -- LAPACK computational routine (version 3.4.0) --  *  -- LAPACK computational routine --
 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --  *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--  *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
 *     November 2011  
 *  *
 *     .. Scalar Arguments ..  *     .. Scalar Arguments ..
       CHARACTER          UPLO        CHARACTER          UPLO
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 *     ..  *     ..
 *     .. Local Scalars ..  *     .. Local Scalars ..
       LOGICAL            LOWER, ROTATE        LOGICAL            LOWER, ROTATE
       INTEGER            I, IDIR, ISUB, ITER, J, LL, LLL, M, MAXIT, NM1,        INTEGER            I, IDIR, ISUB, ITER, ITERDIVN, J, LL, LLL, M,
      $                   NM12, NM13, OLDLL, OLDM       $                   MAXITDIVN, NM1, NM12, NM13, OLDLL, OLDM
       DOUBLE PRECISION   ABSE, ABSS, COSL, COSR, CS, EPS, F, G, H, MU,        DOUBLE PRECISION   ABSE, ABSS, COSL, COSR, CS, EPS, F, G, H, MU,
      $                   OLDCS, OLDSN, R, SHIFT, SIGMN, SIGMX, SINL,       $                   OLDCS, OLDSN, R, SHIFT, SIGMN, SIGMX, SINL,
      $                   SINR, SLL, SMAX, SMIN, SMINL, SMINOA,       $                   SINR, SLL, SMAX, SMIN, SMINL, SMINOA,
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          CALL DLASQ1( N, D, E, WORK, INFO )           CALL DLASQ1( N, D, E, WORK, INFO )
 *  *
 *     If INFO equals 2, dqds didn't finish, try to finish  *     If INFO equals 2, dqds didn't finish, try to finish
 *           *
          IF( INFO .NE. 2 ) RETURN           IF( INFO .NE. 2 ) RETURN
          INFO = 0           INFO = 0
       END IF        END IF
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    40    CONTINUE     40    CONTINUE
    50    CONTINUE     50    CONTINUE
          SMINOA = SMINOA / SQRT( DBLE( N ) )           SMINOA = SMINOA / SQRT( DBLE( N ) )
          THRESH = MAX( TOL*SMINOA, MAXITR*N*N*UNFL )           THRESH = MAX( TOL*SMINOA, MAXITR*(N*(N*UNFL)) )
       ELSE        ELSE
 *  *
 *        Absolute accuracy desired  *        Absolute accuracy desired
 *  *
          THRESH = MAX( ABS( TOL )*SMAX, MAXITR*N*N*UNFL )           THRESH = MAX( ABS( TOL )*SMAX, MAXITR*(N*(N*UNFL)) )
       END IF        END IF
 *  *
 *     Prepare for main iteration loop for the singular values  *     Prepare for main iteration loop for the singular values
 *     (MAXIT is the maximum number of passes through the inner  *     (MAXIT is the maximum number of passes through the inner
 *     loop permitted before nonconvergence signalled.)  *     loop permitted before nonconvergence signalled.)
 *  *
       MAXIT = MAXITR*N*N        MAXITDIVN = MAXITR*N
       ITER = 0        ITERDIVN = 0
         ITER = -1
       OLDLL = -1        OLDLL = -1
       OLDM = -1        OLDM = -1
 *  *
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 *  *
       IF( M.LE.1 )        IF( M.LE.1 )
      $   GO TO 160       $   GO TO 160
       IF( ITER.GT.MAXIT )  *
      $   GO TO 200        IF( ITER.GE.N ) THEN
            ITER = ITER - N
            ITERDIVN = ITERDIVN + 1
            IF( ITERDIVN.GE.MAXITDIVN )
        $      GO TO 200
         END IF
 *  *
 *     Find diagonal block of matrix to work on  *     Find diagonal block of matrix to work on
 *  *
Removed from v.1.13  
changed lines
  Added in v.1.19

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