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Diff for /rpl/lapack/lapack/dla_gbrfsx_extended.f between versions 1.7 and 1.16

version 1.7, 2012/08/22 09:48:15 version 1.16, 2020/05/21 21:45:57
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 *> \brief \b DLA_GBRFSX_EXTENDED  *> \brief \b DLA_GBRFSX_EXTENDED improves the computed solution to a system of linear equations for general banded matrices by performing extra-precise iterative refinement and provides error bounds and backward error estimates for the solution.
 *  *
 *  =========== 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 DLA_GBRFSX_EXTENDED + dependencies   *> Download DLA_GBRFSX_EXTENDED + dependencies
 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dla_gbrfsx_extended.f">   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dla_gbrfsx_extended.f">
 *> [TGZ]</a>   *> [TGZ]</a>
 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dla_gbrfsx_extended.f">   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dla_gbrfsx_extended.f">
 *> [ZIP]</a>   *> [ZIP]</a>
 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dla_gbrfsx_extended.f">   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dla_gbrfsx_extended.f">
 *> [TXT]</a>  *> [TXT]</a>
 *> \endhtmlonly   *> \endhtmlonly
 *  *
 *  Definition:  *  Definition:
 *  ===========  *  ===========
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 *                                       ERR_BNDS_COMP, RES, AYB, DY,  *                                       ERR_BNDS_COMP, RES, AYB, DY,
 *                                       Y_TAIL, RCOND, ITHRESH, RTHRESH,  *                                       Y_TAIL, RCOND, ITHRESH, RTHRESH,
 *                                       DZ_UB, IGNORE_CWISE, INFO )  *                                       DZ_UB, IGNORE_CWISE, INFO )
 *   *
 *       .. Scalar Arguments ..  *       .. Scalar Arguments ..
 *       INTEGER            INFO, LDAB, LDAFB, LDB, LDY, N, KL, KU, NRHS,  *       INTEGER            INFO, LDAB, LDAFB, LDB, LDY, N, KL, KU, NRHS,
 *      $                   PREC_TYPE, TRANS_TYPE, N_NORMS, ITHRESH  *      $                   PREC_TYPE, TRANS_TYPE, N_NORMS, ITHRESH
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 *      $                   ERR_BNDS_NORM( NRHS, * ),  *      $                   ERR_BNDS_NORM( NRHS, * ),
 *      $                   ERR_BNDS_COMP( NRHS, * )  *      $                   ERR_BNDS_COMP( NRHS, * )
 *       ..  *       ..
 *    *
 *  *
 *> \par Purpose:  *> \par Purpose:
 *  =============  *  =============
 *>  *>
 *> \verbatim  *> \verbatim
 *>  *>
 *>   *>
 *> DLA_GBRFSX_EXTENDED improves the computed solution to a system of  *> DLA_GBRFSX_EXTENDED improves the computed solution to a system of
 *> linear equations by performing extra-precise iterative refinement  *> linear equations by performing extra-precise iterative refinement
 *> and provides error bounds and backward error estimates for the solution.  *> and provides error bounds and backward error estimates for the solution.
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 *> \verbatim  *> \verbatim
 *>          PREC_TYPE is INTEGER  *>          PREC_TYPE is INTEGER
 *>     Specifies the intermediate precision to be used in refinement.  *>     Specifies the intermediate precision to be used in refinement.
 *>     The value is defined by ILAPREC(P) where P is a CHARACTER and  *>     The value is defined by ILAPREC(P) where P is a CHARACTER and P
 *>     P    = 'S':  Single  *>          = 'S':  Single
 *>          = 'D':  Double  *>          = 'D':  Double
 *>          = 'I':  Indigenous  *>          = 'I':  Indigenous
 *>          = 'X', 'E':  Extra  *>          = 'X' or 'E':  Extra
 *> \endverbatim  *> \endverbatim
 *>  *>
 *> \param[in] TRANS_TYPE  *> \param[in] TRANS_TYPE
 *> \verbatim  *> \verbatim
 *>          TRANS_TYPE is INTEGER  *>          TRANS_TYPE is INTEGER
 *>     Specifies the transposition operation on A.  *>     Specifies the transposition operation on A.
 *>     The value is defined by ILATRANS(T) where T is a CHARACTER and  *>     The value is defined by ILATRANS(T) where T is a CHARACTER and T
 *>     T    = 'N':  No transpose  *>          = 'N':  No transpose
 *>          = 'T':  Transpose  *>          = 'T':  Transpose
 *>          = 'C':  Conjugate transpose  *>          = 'C':  Conjugate transpose
 *> \endverbatim  *> \endverbatim
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 *>  *>
 *> \param[in,out] Y  *> \param[in,out] Y
 *> \verbatim  *> \verbatim
 *>          Y is DOUBLE PRECISION array, dimension  *>          Y is DOUBLE PRECISION array, dimension (LDY,NRHS)
 *>                    (LDY,NRHS)  
 *>     On entry, the solution matrix X, as computed by DGBTRS.  *>     On entry, the solution matrix X, as computed by DGBTRS.
 *>     On exit, the improved solution matrix Y.  *>     On exit, the improved solution matrix Y.
 *> \endverbatim  *> \endverbatim
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 *>  *>
 *> \param[in,out] ERR_BNDS_NORM  *> \param[in,out] ERR_BNDS_NORM
 *> \verbatim  *> \verbatim
 *>          ERR_BNDS_NORM is DOUBLE PRECISION array, dimension  *>          ERR_BNDS_NORM is DOUBLE PRECISION array, dimension (NRHS, N_ERR_BNDS)
 *>                    (NRHS, N_ERR_BNDS)  
 *>     For each right-hand side, this array contains information about  *>     For each right-hand side, this array contains information about
 *>     various error bounds and condition numbers corresponding to the  *>     various error bounds and condition numbers corresponding to the
 *>     normwise relative error, which is defined as follows:  *>     normwise relative error, which is defined as follows:
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 *>  *>
 *> \param[in,out] ERR_BNDS_COMP  *> \param[in,out] ERR_BNDS_COMP
 *> \verbatim  *> \verbatim
 *>          ERR_BNDS_COMP is DOUBLE PRECISION array, dimension  *>          ERR_BNDS_COMP is DOUBLE PRECISION array, dimension (NRHS, N_ERR_BNDS)
 *>                    (NRHS, N_ERR_BNDS)  
 *>     For each right-hand side, this array contains information about  *>     For each right-hand side, this array contains information about
 *>     various error bounds and condition numbers corresponding to the  *>     various error bounds and condition numbers corresponding to the
 *>     componentwise relative error, which is defined as follows:  *>     componentwise relative error, which is defined as follows:
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 *>     information as described below. There currently are up to three  *>     information as described below. There currently are up to three
 *>     pieces of information returned for each right-hand side. If  *>     pieces of information returned for each right-hand side. If
 *>     componentwise accuracy is not requested (PARAMS(3) = 0.0), then  *>     componentwise accuracy is not requested (PARAMS(3) = 0.0), then
 *>     ERR_BNDS_COMP is not accessed.  If N_ERR_BNDS .LT. 3, then at most  *>     ERR_BNDS_COMP is not accessed.  If N_ERR_BNDS < 3, then at most
 *>     the first (:,N_ERR_BNDS) entries are returned.  *>     the first (:,N_ERR_BNDS) entries are returned.
 *>  *>
 *>     The first index in ERR_BNDS_COMP(i,:) corresponds to the ith  *>     The first index in ERR_BNDS_COMP(i,:) corresponds to the ith
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 *  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  *> \date June 2017
 *  *
 *> \ingroup doubleGBcomputational  *> \ingroup doubleGBcomputational
 *  *
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      $                                Y_TAIL, RCOND, ITHRESH, RTHRESH,       $                                Y_TAIL, RCOND, ITHRESH, RTHRESH,
      $                                DZ_UB, IGNORE_CWISE, INFO )       $                                DZ_UB, IGNORE_CWISE, INFO )
 *  *
 *  -- LAPACK computational routine (version 3.4.0) --  *  -- LAPACK computational routine (version 3.7.1) --
 *  -- 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  *     June 2017
 *  *
 *     .. Scalar Arguments ..  *     .. Scalar Arguments ..
       INTEGER            INFO, LDAB, LDAFB, LDB, LDY, N, KL, KU, NRHS,        INTEGER            INFO, LDAB, LDAFB, LDB, LDY, N, KL, KU, NRHS,
Removed from v.1.7  
changed lines
  Added in v.1.16

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