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version 1.6, 2011/11/21 22:19:28 version 1.16, 2023/08/07 08:38:50
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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 DGESVXX + dependencies   *> Download DGESVXX + dependencies
 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dgesvxx.f">   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dgesvxx.f">
 *> [TGZ]</a>   *> [TGZ]</a>
 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dgesvxx.f">   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dgesvxx.f">
 *> [ZIP]</a>   *> [ZIP]</a>
 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dgesvxx.f">   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dgesvxx.f">
 *> [TXT]</a>  *> [TXT]</a>
 *> \endhtmlonly   *> \endhtmlonly
 *  *
 *  Definition:  *  Definition:
 *  ===========  *  ===========
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 *                           BERR, N_ERR_BNDS, ERR_BNDS_NORM,  *                           BERR, N_ERR_BNDS, ERR_BNDS_NORM,
 *                           ERR_BNDS_COMP, NPARAMS, PARAMS, WORK, IWORK,  *                           ERR_BNDS_COMP, NPARAMS, PARAMS, WORK, IWORK,
 *                           INFO )  *                           INFO )
 *   *
 *       .. Scalar Arguments ..  *       .. Scalar Arguments ..
 *       CHARACTER          EQUED, FACT, TRANS  *       CHARACTER          EQUED, FACT, TRANS
 *       INTEGER            INFO, LDA, LDAF, LDB, LDX, N, NRHS, NPARAMS,  *       INTEGER            INFO, LDA, LDAF, LDB, LDX, N, NRHS, NPARAMS,
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 *      $                   ERR_BNDS_NORM( NRHS, * ),  *      $                   ERR_BNDS_NORM( NRHS, * ),
 *      $                   ERR_BNDS_COMP( NRHS, * )  *      $                   ERR_BNDS_COMP( NRHS, * )
 *       ..  *       ..
 *    *
 *  *
 *> \par Purpose:  *> \par Purpose:
 *  =============  *  =============
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 *>  *>
 *> \param[in,out] AF  *> \param[in,out] AF
 *> \verbatim  *> \verbatim
 *>          AF is or output) DOUBLE PRECISION array, dimension (LDAF,N)  *>          AF is DOUBLE PRECISION array, dimension (LDAF,N)
 *>     If FACT = 'F', then AF is an input argument and on entry  *>     If FACT = 'F', then AF is an input argument and on entry
 *>     contains the factors L and U from the factorization  *>     contains the factors L and U from the factorization
 *>     A = P*L*U as computed by DGETRF.  If EQUED .ne. 'N', then  *>     A = P*L*U as computed by DGETRF.  If EQUED .ne. 'N', then
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 *>  *>
 *> \param[in,out] IPIV  *> \param[in,out] IPIV
 *> \verbatim  *> \verbatim
 *>          IPIV is or output) INTEGER array, dimension (N)  *>          IPIV is INTEGER array, dimension (N)
 *>     If FACT = 'F', then IPIV is an input argument and on entry  *>     If FACT = 'F', then IPIV is an input argument and on entry
 *>     contains the pivot indices from the factorization A = P*L*U  *>     contains the pivot indices from the factorization A = P*L*U
 *>     as computed by DGETRF; row i of the matrix was interchanged  *>     as computed by DGETRF; row i of the matrix was interchanged
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 *>  *>
 *> \param[in,out] EQUED  *> \param[in,out] EQUED
 *> \verbatim  *> \verbatim
 *>          EQUED is or output) CHARACTER*1  *>          EQUED is CHARACTER*1
 *>     Specifies the form of equilibration that was done.  *>     Specifies the form of equilibration that was done.
 *>       = 'N':  No equilibration (always true if FACT = 'N').  *>       = 'N':  No equilibration (always true if FACT = 'N').
 *>       = 'R':  Row equilibration, i.e., A has been premultiplied by  *>       = 'R':  Row equilibration, i.e., A has been premultiplied by
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 *>  *>
 *> \param[in,out] R  *> \param[in,out] R
 *> \verbatim  *> \verbatim
 *>          R is or output) DOUBLE PRECISION array, dimension (N)  *>          R is DOUBLE PRECISION array, dimension (N)
 *>     The row scale factors for A.  If EQUED = 'R' or 'B', A is  *>     The row scale factors for A.  If EQUED = 'R' or 'B', A is
 *>     multiplied on the left by diag(R); if EQUED = 'N' or 'C', R  *>     multiplied on the left by diag(R); if EQUED = 'N' or 'C', R
 *>     is not accessed.  R is an input argument if FACT = 'F';  *>     is not accessed.  R is an input argument if FACT = 'F';
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 *>  *>
 *> \param[in,out] C  *> \param[in,out] C
 *> \verbatim  *> \verbatim
 *>          C is or output) DOUBLE PRECISION array, dimension (N)  *>          C is DOUBLE PRECISION array, dimension (N)
 *>     The column scale factors for A.  If EQUED = 'C' or 'B', A is  *>     The column scale factors for A.  If EQUED = 'C' or 'B', A is
 *>     multiplied on the right by diag(C); if EQUED = 'N' or 'R', C  *>     multiplied on the right by diag(C); if EQUED = 'N' or 'R', C
 *>     is not accessed.  C is an input argument if FACT = 'F';  *>     is not accessed.  C is an input argument if FACT = 'F';
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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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 *> \param[in] NPARAMS  *> \param[in] NPARAMS
 *> \verbatim  *> \verbatim
 *>          NPARAMS is INTEGER  *>          NPARAMS is INTEGER
 *>     Specifies the number of parameters set in PARAMS.  If .LE. 0, the  *>     Specifies the number of parameters set in PARAMS.  If <= 0, the
 *>     PARAMS array is never referenced and default values are used.  *>     PARAMS array is never referenced and default values are used.
 *> \endverbatim  *> \endverbatim
 *>  *>
 *> \param[in,out] PARAMS  *> \param[in,out] PARAMS
 *> \verbatim  *> \verbatim
 *>          PARAMS is / output) DOUBLE PRECISION array, dimension (NPARAMS)  *>          PARAMS is DOUBLE PRECISION array, dimension (NPARAMS)
 *>     Specifies algorithm parameters.  If an entry is .LT. 0.0, then  *>     Specifies algorithm parameters.  If an entry is < 0.0, then
 *>     that entry will be filled with default value used for that  *>     that entry will be filled with default value used for that
 *>     parameter.  Only positions up to NPARAMS are accessed; defaults  *>     parameter.  Only positions up to NPARAMS are accessed; defaults
 *>     are used for higher-numbered parameters.  *>     are used for higher-numbered parameters.
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 *>       PARAMS(LA_LINRX_ITREF_I = 1) : Whether to perform iterative  *>       PARAMS(LA_LINRX_ITREF_I = 1) : Whether to perform iterative
 *>            refinement or not.  *>            refinement or not.
 *>         Default: 1.0D+0  *>         Default: 1.0D+0
 *>            = 0.0 : No refinement is performed, and no error bounds are  *>            = 0.0:  No refinement is performed, and no error bounds are
 *>                    computed.  *>                    computed.
 *>            = 1.0 : Use the extra-precise refinement algorithm.  *>            = 1.0:  Use the extra-precise refinement algorithm.
 *>              (other values are reserved for future use)  *>              (other values are reserved for future use)
 *>  *>
 *>       PARAMS(LA_LINRX_ITHRESH_I = 2) : Maximum number of residual  *>       PARAMS(LA_LINRX_ITHRESH_I = 2) : Maximum number of residual
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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  
 *  *
 *> \ingroup doubleGEsolve  *> \ingroup doubleGEsolve
 *  *
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      $                    ERR_BNDS_COMP, NPARAMS, PARAMS, WORK, IWORK,       $                    ERR_BNDS_COMP, NPARAMS, PARAMS, WORK, IWORK,
      $                    INFO )       $                    INFO )
 *  *
 *  -- LAPACK driver routine (version 3.4.0) --  *  -- LAPACK driver 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          EQUED, FACT, TRANS        CHARACTER          EQUED, FACT, TRANS
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      $                   SMLNUM       $                   SMLNUM
 *     ..  *     ..
 *     .. External Functions ..  *     .. External Functions ..
       EXTERNAL           LSAME, DLAMCH, DLA_RPVGRW        EXTERNAL           LSAME, DLAMCH, DLA_GERPVGRW
       LOGICAL            LSAME        LOGICAL            LSAME
       DOUBLE PRECISION   DLAMCH, DLA_RPVGRW        DOUBLE PRECISION   DLAMCH, DLA_GERPVGRW
 *     ..  *     ..
 *     .. External Subroutines ..  *     .. External Subroutines ..
       EXTERNAL           DGEEQUB, DGETRF, DGETRS, DLACPY, DLAQGE,        EXTERNAL           DGEEQUB, DGETRF, DGETRS, DLACPY, DLAQGE,
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 *           Compute the reciprocal pivot growth factor of the  *           Compute the reciprocal pivot growth factor of the
 *           leading rank-deficient INFO columns of A.  *           leading rank-deficient INFO columns of A.
 *  *
             RPVGRW = DLA_RPVGRW( N, INFO, A, LDA, AF, LDAF )              RPVGRW = DLA_GERPVGRW( N, INFO, A, LDA, AF, LDAF )
             RETURN              RETURN
          END IF           END IF
       END IF        END IF
 *  *
 *     Compute the reciprocal pivot growth factor RPVGRW.  *     Compute the reciprocal pivot growth factor RPVGRW.
 *  *
       RPVGRW = DLA_RPVGRW( N, N, A, LDA, AF, LDAF )        RPVGRW = DLA_GERPVGRW( N, N, A, LDA, AF, LDAF )
 *  *
 *     Compute the solution matrix X.  *     Compute the solution matrix X.
 *  *
Removed from v.1.6  
changed lines
  Added in v.1.16

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