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Diff for /rpl/lapack/lapack/dla_syrfsx_extended.f between versions 1.7 and 1.17

version 1.7, 2012/07/31 11:06:35 version 1.17, 2020/05/21 21:45:58
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 *> \brief \b DLA_SYRFSX_EXTENDED  *> \brief \b DLA_SYRFSX_EXTENDED improves the computed solution to a system of linear equations for symmetric indefinite 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_SYRFSX_EXTENDED + dependencies   *> Download DLA_SYRFSX_EXTENDED + dependencies
 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dla_syrfsx_extended.f">   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dla_syrfsx_extended.f">
 *> [TGZ]</a>   *> [TGZ]</a>
 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dla_syrfsx_extended.f">   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dla_syrfsx_extended.f">
 *> [ZIP]</a>   *> [ZIP]</a>
 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dla_syrfsx_extended.f">   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dla_syrfsx_extended.f">
 *> [TXT]</a>  *> [TXT]</a>
 *> \endhtmlonly   *> \endhtmlonly
 *  *
 *  Definition:  *  Definition:
 *  ===========  *  ===========
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 *                                       AYB, DY, Y_TAIL, RCOND, ITHRESH,  *                                       AYB, DY, Y_TAIL, RCOND, ITHRESH,
 *                                       RTHRESH, DZ_UB, IGNORE_CWISE,  *                                       RTHRESH, DZ_UB, IGNORE_CWISE,
 *                                       INFO )  *                                       INFO )
 *   *
 *       .. Scalar Arguments ..  *       .. Scalar Arguments ..
 *       INTEGER            INFO, LDA, LDAF, LDB, LDY, N, NRHS, PREC_TYPE,  *       INTEGER            INFO, LDA, LDAF, LDB, LDY, N, NRHS, PREC_TYPE,
 *      $                   N_NORMS, ITHRESH  *      $                   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_SYRFSX_EXTENDED improves the computed solution to a system of  *> DLA_SYRFSX_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] UPLO  *> \param[in] UPLO
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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 DSYTRS.  *>     On entry, the solution matrix X, as computed by DSYTRS.
 *>     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 doubleSYcomputational  *> \ingroup doubleSYcomputational
 *  *
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      $                                RTHRESH, DZ_UB, IGNORE_CWISE,       $                                RTHRESH, DZ_UB, IGNORE_CWISE,
      $                                INFO )       $                                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, LDA, LDAF, LDB, LDY, N, NRHS, PREC_TYPE,        INTEGER            INFO, LDA, LDAF, LDB, LDY, N, NRHS, PREC_TYPE,
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                CALL BLAS_DSYMV2_X(UPLO2, N, -1.0D+0, A, LDA,                 CALL BLAS_DSYMV2_X(UPLO2, N, -1.0D+0, A, LDA,
      $              Y(1, J), Y_TAIL, 1, 1.0D+0, RES, 1, PREC_TYPE)       $              Y(1, J), Y_TAIL, 1, 1.0D+0, RES, 1, PREC_TYPE)
             END IF              END IF
               
 !         XXX: RES is no longer needed.  !         XXX: RES is no longer needed.
             CALL DCOPY( N, RES, 1, DY, 1 )              CALL DCOPY( N, RES, 1, DY, 1 )
             CALL DSYTRS( UPLO, N, 1, AF, LDAF, IPIV, DY, N, INFO )              CALL DSYTRS( UPLO, N, 1, AF, LDAF, IPIV, DY, N, INFO )
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             NORMDX = 0.0D+0              NORMDX = 0.0D+0
             DZ_Z = 0.0D+0              DZ_Z = 0.0D+0
             YMIN = HUGEVAL              YMIN = HUGEVAL
               
             DO I = 1, N              DO I = 1, N
                YK = ABS( Y( I, J ) )                 YK = ABS( Y( I, J ) )
                DYK = ABS( DY( I ) )                 DYK = ABS( DY( I ) )
                  
                IF ( YK .NE. 0.0D+0 ) THEN                 IF ( YK .NE. 0.0D+0 ) THEN
                   DZ_Z = MAX( DZ_Z, DYK / YK )                    DZ_Z = MAX( DZ_Z, DYK / YK )
                ELSE IF ( DYK .NE. 0.0D+0 ) THEN                 ELSE IF ( DYK .NE. 0.0D+0 ) THEN
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             ELSE              ELSE
                CALL DLA_WWADDW( N, Y(1,J), Y_TAIL, DY )                 CALL DLA_WWADDW( N, Y(1,J), Y_TAIL, DY )
             END IF              END IF
               
          END DO           END DO
 *        Target of "IF (Z_STOP .AND. X_STOP)".  Sun's f77 won't EXIT.  *        Target of "IF (Z_STOP .AND. X_STOP)".  Sun's f77 won't EXIT.
  666     CONTINUE   666     CONTINUE
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 *        Compute residual RES = B_s - op(A_s) * Y,  *        Compute residual RES = B_s - op(A_s) * Y,
 *            op(A) = A, A**T, or A**H depending on TRANS (and type).  *            op(A) = A, A**T, or A**H depending on TRANS (and type).
          CALL DCOPY( N, B( 1, J ), 1, RES, 1 )           CALL DCOPY( N, B( 1, J ), 1, RES, 1 )
          CALL DSYMV( UPLO, N, -1.0D+0, A, LDA, Y(1,J), 1, 1.0D+0, RES,            CALL DSYMV( UPLO, N, -1.0D+0, A, LDA, Y(1,J), 1, 1.0D+0, RES,
      $     1 )       $     1 )
            
          DO I = 1, N           DO I = 1, N
             AYB( I ) = ABS( B( I, J ) )              AYB( I ) = ABS( B( I, J ) )
          END DO           END DO
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 *  *
          CALL DLA_SYAMV( UPLO2, N, 1.0D+0,           CALL DLA_SYAMV( UPLO2, N, 1.0D+0,
      $        A, LDA, Y(1, J), 1, 1.0D+0, AYB, 1 )       $        A, LDA, Y(1, J), 1, 1.0D+0, AYB, 1 )
            
          CALL DLA_LIN_BERR( N, N, 1, RES, AYB, BERR_OUT( J ) )           CALL DLA_LIN_BERR( N, N, 1, RES, AYB, BERR_OUT( J ) )
 *  *
 *     End of loop for each RHS.  *     End of loop for each RHS.
Removed from v.1.7  
changed lines
  Added in v.1.17

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