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version 1.10, 2014/01/27 09:28:31 version 1.17, 2023/08/07 08:39:15
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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 ZGBRFSX + dependencies   *> Download ZGBRFSX + dependencies
 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zgbrfsx.f">   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zgbrfsx.f">
 *> [TGZ]</a>   *> [TGZ]</a>
 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zgbrfsx.f">   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zgbrfsx.f">
 *> [ZIP]</a>   *> [ZIP]</a>
 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zgbrfsx.f">   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zgbrfsx.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, RWORK,  *                           ERR_BNDS_COMP, NPARAMS, PARAMS, WORK, RWORK,
 *                           INFO )  *                           INFO )
 *   *
 *       .. Scalar Arguments ..  *       .. Scalar Arguments ..
 *       CHARACTER          TRANS, EQUED  *       CHARACTER          TRANS, EQUED
 *       INTEGER            INFO, LDAB, LDAFB, LDB, LDX, N, KL, KU, NRHS,  *       INTEGER            INFO, LDAB, LDAFB, LDB, LDX, N, KL, KU, NRHS,
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 *      $                   ERR_BNDS_NORM( NRHS, * ),  *      $                   ERR_BNDS_NORM( NRHS, * ),
 *      $                   ERR_BNDS_COMP( NRHS, * ), RWORK( * )  *      $                   ERR_BNDS_COMP( NRHS, * ), RWORK( * )
 *       ..  *       ..
 *    *
 *  *
 *> \par Purpose:  *> \par Purpose:
 *  =============  *  =============
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 *>     Specifies the form of the system of equations:  *>     Specifies the form of the system of equations:
 *>       = 'N':  A * X = B     (No transpose)  *>       = 'N':  A * X = B     (No transpose)
 *>       = 'T':  A**T * X = B  (Transpose)  *>       = 'T':  A**T * X = B  (Transpose)
 *>       = 'C':  A**H * X = B  (Conjugate transpose = Transpose)  *>       = 'C':  A**H * X = B  (Conjugate transpose)
 *> \endverbatim  *> \endverbatim
 *>  *>
 *> \param[in] EQUED  *> \param[in] EQUED
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 *> \verbatim  *> \verbatim
 *>          AFB is COMPLEX*16 array, dimension (LDAFB,N)  *>          AFB is COMPLEX*16 array, dimension (LDAFB,N)
 *>     Details of the LU factorization of the band matrix A, as  *>     Details of the LU factorization of the band matrix A, as
 *>     computed by DGBTRF.  U is stored as an upper triangular band  *>     computed by ZGBTRF.  U is stored as an upper triangular band
 *>     matrix with KL+KU superdiagonals in rows 1 to KL+KU+1, and  *>     matrix with KL+KU superdiagonals in rows 1 to KL+KU+1, and
 *>     the multipliers used during the factorization are stored in  *>     the multipliers used during the factorization are stored in
 *>     rows KL+KU+2 to 2*KL+KU+1.  *>     rows KL+KU+2 to 2*KL+KU+1.
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 *> \param[in] IPIV  *> \param[in] IPIV
 *> \verbatim  *> \verbatim
 *>          IPIV is INTEGER array, dimension (N)  *>          IPIV is INTEGER array, dimension (N)
 *>     The pivot indices from DGETRF; for 1<=i<=N, row i of the  *>     The pivot indices from ZGETRF; for 1<=i<=N, row i of the
 *>     matrix was interchanged with row IPIV(i).  *>     matrix was interchanged with row IPIV(i).
 *> \endverbatim  *> \endverbatim
 *>  *>
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 *>  *>
 *> \param[in] B  *> \param[in] B
 *> \verbatim  *> \verbatim
 *>          B is DOUBLE PRECISION array, dimension (LDB,NRHS)  *>          B is COMPLEX*16 array, dimension (LDB,NRHS)
 *>     The right hand side matrix B.  *>     The right hand side matrix B.
 *> \endverbatim  *> \endverbatim
 *>  *>
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 *> \param[in,out] X  *> \param[in,out] X
 *> \verbatim  *> \verbatim
 *>          X is COMPLEX*16 array, dimension (LDX,NRHS)  *>          X is COMPLEX*16 array, dimension (LDX,NRHS)
 *>     On entry, the solution matrix X, as computed by DGETRS.  *>     On entry, the solution matrix X, as computed by ZGETRS.
 *>     On exit, the improved solution matrix X.  *>     On exit, the improved solution matrix X.
 *> \endverbatim  *> \endverbatim
 *>  *>
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 *>  *>
 *> \param[out] BERR  *> \param[out] BERR
 *> \verbatim  *> \verbatim
 *>          BERR is COMPLEX*16 array, dimension (NRHS)  *>          BERR is DOUBLE PRECISION array, dimension (NRHS)
 *>     Componentwise relative backward error.  This is the  *>     Componentwise relative backward error.  This is the
 *>     componentwise relative backward error of each solution vector X(j)  *>     componentwise relative backward error of each solution vector X(j)
 *>     (i.e., the smallest relative change in any element of A or B that  *>     (i.e., the smallest relative change in any element of A or B that
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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 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 double-precision refinement algorithm,  *>            = 1.0:  Use the double-precision refinement algorithm,
 *>                    possibly with doubled-single computations if the  *>                    possibly with doubled-single computations if the
 *>                    compilation environment does not support DOUBLE  *>                    compilation environment does not support DOUBLE
 *>                    PRECISION.  *>                    PRECISION.
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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 April 2012  
 *  *
 *> \ingroup complex16GBcomputational  *> \ingroup complex16GBcomputational
 *  *
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      $                    ERR_BNDS_COMP, NPARAMS, PARAMS, WORK, RWORK,       $                    ERR_BNDS_COMP, NPARAMS, PARAMS, WORK, RWORK,
      $                    INFO )       $                    INFO )
 *  *
 *  -- LAPACK computational routine (version 3.4.1) --  *  -- 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..--
 *     April 2012  
 *  *
 *     .. Scalar Arguments ..  *     .. Scalar Arguments ..
       CHARACTER          TRANS, EQUED        CHARACTER          TRANS, EQUED
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       INTRINSIC          MAX, SQRT, TRANSFER        INTRINSIC          MAX, SQRT, TRANSFER
 *     ..  *     ..
 *     .. External Functions ..  *     .. External Functions ..
       EXTERNAL           LSAME, BLAS_FPINFO_X, ILATRANS, ILAPREC        EXTERNAL           LSAME, ILAPREC
       EXTERNAL           DLAMCH, ZLANGB, ZLA_GBRCOND_X, ZLA_GBRCOND_C        EXTERNAL           DLAMCH, ZLANGB, ZLA_GBRCOND_X, ZLA_GBRCOND_C
       DOUBLE PRECISION   DLAMCH, ZLANGB, ZLA_GBRCOND_X, ZLA_GBRCOND_C        DOUBLE PRECISION   DLAMCH, ZLANGB, ZLA_GBRCOND_X, ZLA_GBRCOND_C
       LOGICAL            LSAME        LOGICAL            LSAME
       INTEGER            BLAS_FPINFO_X  
       INTEGER            ILATRANS, ILAPREC        INTEGER            ILATRANS, ILAPREC
 *     ..  *     ..
 *     .. Executable Statements ..  *     .. Executable Statements ..
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 *  *
 *     Perform refinement on each right-hand side  *     Perform refinement on each right-hand side
 *  *
       IF ( REF_TYPE .NE. 0 ) THEN        IF ( REF_TYPE .NE. 0 .AND. INFO .EQ. 0 ) THEN
   
          PREC_TYPE = ILAPREC( 'E' )           PREC_TYPE = ILAPREC( 'E' )
   
Removed from v.1.10  
changed lines
  Added in v.1.17

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