[BACK]Return to dlaic1.f CVS log [TXT] [DIR] Up to [local] / rpl / lapack / lapack

Diff for /rpl/lapack/lapack/dlaic1.f between versions 1.8 and 1.9

version 1.8, 2011/07/22 07:38:06 version 1.9, 2011/11/21 20:42:55
Line 1 Line 1
   *> \brief \b DLAIC1
   *
   *  =========== DOCUMENTATION ===========
   *
   * Online html documentation available at 
   *            http://www.netlib.org/lapack/explore-html/ 
   *
   *> \htmlonly
   *> Download DLAIC1 + dependencies 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlaic1.f"> 
   *> [TGZ]</a> 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlaic1.f"> 
   *> [ZIP]</a> 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlaic1.f"> 
   *> [TXT]</a>
   *> \endhtmlonly 
   *
   *  Definition:
   *  ===========
   *
   *       SUBROUTINE DLAIC1( JOB, J, X, SEST, W, GAMMA, SESTPR, S, C )
   * 
   *       .. Scalar Arguments ..
   *       INTEGER            J, JOB
   *       DOUBLE PRECISION   C, GAMMA, S, SEST, SESTPR
   *       ..
   *       .. Array Arguments ..
   *       DOUBLE PRECISION   W( J ), X( J )
   *       ..
   *  
   *
   *> \par Purpose:
   *  =============
   *>
   *> \verbatim
   *>
   *> DLAIC1 applies one step of incremental condition estimation in
   *> its simplest version:
   *>
   *> Let x, twonorm(x) = 1, be an approximate singular vector of an j-by-j
   *> lower triangular matrix L, such that
   *>          twonorm(L*x) = sest
   *> Then DLAIC1 computes sestpr, s, c such that
   *> the vector
   *>                 [ s*x ]
   *>          xhat = [  c  ]
   *> is an approximate singular vector of
   *>                 [ L       0  ]
   *>          Lhat = [ w**T gamma ]
   *> in the sense that
   *>          twonorm(Lhat*xhat) = sestpr.
   *>
   *> Depending on JOB, an estimate for the largest or smallest singular
   *> value is computed.
   *>
   *> Note that [s c]**T and sestpr**2 is an eigenpair of the system
   *>
   *>     diag(sest*sest, 0) + [alpha  gamma] * [ alpha ]
   *>                                           [ gamma ]
   *>
   *> where  alpha =  x**T*w.
   *> \endverbatim
   *
   *  Arguments:
   *  ==========
   *
   *> \param[in] JOB
   *> \verbatim
   *>          JOB is INTEGER
   *>          = 1: an estimate for the largest singular value is computed.
   *>          = 2: an estimate for the smallest singular value is computed.
   *> \endverbatim
   *>
   *> \param[in] J
   *> \verbatim
   *>          J is INTEGER
   *>          Length of X and W
   *> \endverbatim
   *>
   *> \param[in] X
   *> \verbatim
   *>          X is DOUBLE PRECISION array, dimension (J)
   *>          The j-vector x.
   *> \endverbatim
   *>
   *> \param[in] SEST
   *> \verbatim
   *>          SEST is DOUBLE PRECISION
   *>          Estimated singular value of j by j matrix L
   *> \endverbatim
   *>
   *> \param[in] W
   *> \verbatim
   *>          W is DOUBLE PRECISION array, dimension (J)
   *>          The j-vector w.
   *> \endverbatim
   *>
   *> \param[in] GAMMA
   *> \verbatim
   *>          GAMMA is DOUBLE PRECISION
   *>          The diagonal element gamma.
   *> \endverbatim
   *>
   *> \param[out] SESTPR
   *> \verbatim
   *>          SESTPR is DOUBLE PRECISION
   *>          Estimated singular value of (j+1) by (j+1) matrix Lhat.
   *> \endverbatim
   *>
   *> \param[out] S
   *> \verbatim
   *>          S is DOUBLE PRECISION
   *>          Sine needed in forming xhat.
   *> \endverbatim
   *>
   *> \param[out] C
   *> \verbatim
   *>          C is DOUBLE PRECISION
   *>          Cosine needed in forming xhat.
   *> \endverbatim
   *
   *  Authors:
   *  ========
   *
   *> \author Univ. of Tennessee 
   *> \author Univ. of California Berkeley 
   *> \author Univ. of Colorado Denver 
   *> \author NAG Ltd. 
   *
   *> \date November 2011
   *
   *> \ingroup doubleOTHERauxiliary
   *
   *  =====================================================================
       SUBROUTINE DLAIC1( JOB, J, X, SEST, W, GAMMA, SESTPR, S, C )        SUBROUTINE DLAIC1( JOB, J, X, SEST, W, GAMMA, SESTPR, S, C )
 *  *
 *  -- LAPACK auxiliary routine (version 3.3.1) --  *  -- LAPACK auxiliary routine (version 3.4.0) --
 *  -- 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..--
 *  -- April 2011                                                      --  *     November 2011
 *  *
 *     .. Scalar Arguments ..  *     .. Scalar Arguments ..
       INTEGER            J, JOB        INTEGER            J, JOB
Line 13 Line 147
       DOUBLE PRECISION   W( J ), X( J )        DOUBLE PRECISION   W( J ), X( J )
 *     ..  *     ..
 *  *
 *  Purpose  
 *  =======  
 *  
 *  DLAIC1 applies one step of incremental condition estimation in  
 *  its simplest version:  
 *  
 *  Let x, twonorm(x) = 1, be an approximate singular vector of an j-by-j  
 *  lower triangular matrix L, such that  
 *           twonorm(L*x) = sest  
 *  Then DLAIC1 computes sestpr, s, c such that  
 *  the vector  
 *                  [ s*x ]  
 *           xhat = [  c  ]  
 *  is an approximate singular vector of  
 *                  [ L       0  ]  
 *           Lhat = [ w**T gamma ]  
 *  in the sense that  
 *           twonorm(Lhat*xhat) = sestpr.  
 *  
 *  Depending on JOB, an estimate for the largest or smallest singular  
 *  value is computed.  
 *  
 *  Note that [s c]**T and sestpr**2 is an eigenpair of the system  
 *  
 *      diag(sest*sest, 0) + [alpha  gamma] * [ alpha ]  
 *                                            [ gamma ]  
 *  
 *  where  alpha =  x**T*w.  
 *  
 *  Arguments  
 *  =========  
 *  
 *  JOB     (input) INTEGER  
 *          = 1: an estimate for the largest singular value is computed.  
 *          = 2: an estimate for the smallest singular value is computed.  
 *  
 *  J       (input) INTEGER  
 *          Length of X and W  
 *  
 *  X       (input) DOUBLE PRECISION array, dimension (J)  
 *          The j-vector x.  
 *  
 *  SEST    (input) DOUBLE PRECISION  
 *          Estimated singular value of j by j matrix L  
 *  
 *  W       (input) DOUBLE PRECISION array, dimension (J)  
 *          The j-vector w.  
 *  
 *  GAMMA   (input) DOUBLE PRECISION  
 *          The diagonal element gamma.  
 *  
 *  SESTPR  (output) DOUBLE PRECISION  
 *          Estimated singular value of (j+1) by (j+1) matrix Lhat.  
 *  
 *  S       (output) DOUBLE PRECISION  
 *          Sine needed in forming xhat.  
 *  
 *  C       (output) DOUBLE PRECISION  
 *          Cosine needed in forming xhat.  
 *  
 *  =====================================================================  *  =====================================================================
 *  *
 *     .. Parameters ..  *     .. Parameters ..
Removed from v.1.8  
changed lines
  Added in v.1.9

CVSweb interface <joel.bertrand@systella.fr>