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Annotation of rpl/lapack/lapack/zla_lin_berr.f, revision 1.5

1.5     ! bertrand    1: *> \brief \b ZLA_LIN_BERR
        !             2: *
        !             3: *  =========== DOCUMENTATION ===========
        !             4: *
        !             5: * Online html documentation available at 
        !             6: *            http://www.netlib.org/lapack/explore-html/ 
        !             7: *
        !             8: *> \htmlonly
        !             9: *> Download ZLA_LIN_BERR + dependencies 
        !            10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zla_lin_berr.f"> 
        !            11: *> [TGZ]</a> 
        !            12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zla_lin_berr.f"> 
        !            13: *> [ZIP]</a> 
        !            14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zla_lin_berr.f"> 
        !            15: *> [TXT]</a>
        !            16: *> \endhtmlonly 
        !            17: *
        !            18: *  Definition:
        !            19: *  ===========
        !            20: *
        !            21: *       SUBROUTINE ZLA_LIN_BERR ( N, NZ, NRHS, RES, AYB, BERR )
        !            22: * 
        !            23: *       .. Scalar Arguments ..
        !            24: *       INTEGER            N, NZ, NRHS
        !            25: *       ..
        !            26: *       .. Array Arguments ..
        !            27: *       DOUBLE PRECISION   AYB( N, NRHS ), BERR( NRHS )
        !            28: *       COMPLEX*16         RES( N, NRHS )
        !            29: *       ..
        !            30: *  
        !            31: *
        !            32: *> \par Purpose:
        !            33: *  =============
        !            34: *>
        !            35: *> \verbatim
        !            36: *>
        !            37: *>    ZLA_LIN_BERR computes componentwise relative backward error from
        !            38: *>    the formula
        !            39: *>        max(i) ( abs(R(i)) / ( abs(op(A_s))*abs(Y) + abs(B_s) )(i) )
        !            40: *>    where abs(Z) is the componentwise absolute value of the matrix
        !            41: *>    or vector Z.
        !            42: *> \endverbatim
        !            43: *
        !            44: *  Arguments:
        !            45: *  ==========
        !            46: *
        !            47: *> \param[in] N
        !            48: *> \verbatim
        !            49: *>          N is INTEGER
        !            50: *>     The number of linear equations, i.e., the order of the
        !            51: *>     matrix A.  N >= 0.
        !            52: *> \endverbatim
        !            53: *>
        !            54: *> \param[in] NZ
        !            55: *> \verbatim
        !            56: *>          NZ is INTEGER
        !            57: *>     We add (NZ+1)*SLAMCH( 'Safe minimum' ) to R(i) in the numerator to
        !            58: *>     guard against spuriously zero residuals. Default value is N.
        !            59: *> \endverbatim
        !            60: *>
        !            61: *> \param[in] NRHS
        !            62: *> \verbatim
        !            63: *>          NRHS is INTEGER
        !            64: *>     The number of right hand sides, i.e., the number of columns
        !            65: *>     of the matrices AYB, RES, and BERR.  NRHS >= 0.
        !            66: *> \endverbatim
        !            67: *>
        !            68: *> \param[in] RES
        !            69: *> \verbatim
        !            70: *>          RES is DOUBLE PRECISION array, dimension (N,NRHS)
        !            71: *>     The residual matrix, i.e., the matrix R in the relative backward
        !            72: *>     error formula above.
        !            73: *> \endverbatim
        !            74: *>
        !            75: *> \param[in] AYB
        !            76: *> \verbatim
        !            77: *>          AYB is DOUBLE PRECISION array, dimension (N, NRHS)
        !            78: *>     The denominator in the relative backward error formula above, i.e.,
        !            79: *>     the matrix abs(op(A_s))*abs(Y) + abs(B_s). The matrices A, Y, and B
        !            80: *>     are from iterative refinement (see zla_gerfsx_extended.f).
        !            81: *> \endverbatim
        !            82: *>     
        !            83: *> \param[out] BERR
        !            84: *> \verbatim
        !            85: *>          BERR is COMPLEX*16 array, dimension (NRHS)
        !            86: *>     The componentwise relative backward error from the formula above.
        !            87: *> \endverbatim
        !            88: *
        !            89: *  Authors:
        !            90: *  ========
        !            91: *
        !            92: *> \author Univ. of Tennessee 
        !            93: *> \author Univ. of California Berkeley 
        !            94: *> \author Univ. of Colorado Denver 
        !            95: *> \author NAG Ltd. 
        !            96: *
        !            97: *> \date November 2011
        !            98: *
        !            99: *> \ingroup complex16OTHERcomputational
        !           100: *
        !           101: *  =====================================================================
1.1       bertrand  102:       SUBROUTINE ZLA_LIN_BERR ( N, NZ, NRHS, RES, AYB, BERR )
                    103: *
1.5     ! bertrand  104: *  -- LAPACK computational routine (version 3.4.0) --
        !           105: *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
        !           106: *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
        !           107: *     November 2011
1.1       bertrand  108: *
                    109: *     .. Scalar Arguments ..
                    110:       INTEGER            N, NZ, NRHS
                    111: *     ..
                    112: *     .. Array Arguments ..
                    113:       DOUBLE PRECISION   AYB( N, NRHS ), BERR( NRHS )
                    114:       COMPLEX*16         RES( N, NRHS )
                    115: *     ..
                    116: *
                    117: *  =====================================================================
                    118: *
                    119: *     .. Local Scalars ..
                    120:       DOUBLE PRECISION   TMP
                    121:       INTEGER            I, J
                    122:       COMPLEX*16         CDUM
                    123: *     ..
                    124: *     .. Intrinsic Functions ..
                    125:       INTRINSIC          ABS, REAL, DIMAG, MAX
                    126: *     ..
                    127: *     .. External Functions ..
                    128:       EXTERNAL           DLAMCH
                    129:       DOUBLE PRECISION   DLAMCH
                    130:       DOUBLE PRECISION   SAFE1
                    131: *     ..
                    132: *     .. Statement Functions ..
                    133:       COMPLEX*16         CABS1
                    134: *     ..
                    135: *     .. Statement Function Definitions ..
                    136:       CABS1( CDUM ) = ABS( DBLE( CDUM ) ) + ABS( DIMAG( CDUM ) )
                    137: *     ..
                    138: *     .. Executable Statements ..
                    139: *
                    140: *     Adding SAFE1 to the numerator guards against spuriously zero
                    141: *     residuals.  A similar safeguard is in the CLA_yyAMV routine used
                    142: *     to compute AYB.
                    143: *
                    144:       SAFE1 = DLAMCH( 'Safe minimum' )
                    145:       SAFE1 = (NZ+1)*SAFE1
                    146: 
                    147:       DO J = 1, NRHS
                    148:          BERR(J) = 0.0D+0
                    149:          DO I = 1, N
                    150:             IF (AYB(I,J) .NE. 0.0D+0) THEN
                    151:                TMP = (SAFE1 + CABS1(RES(I,J)))/AYB(I,J)
                    152:                BERR(J) = MAX( BERR(J), TMP )
                    153:             END IF
                    154: *
                    155: *     If AYB is exactly 0.0 (and if computed by CLA_yyAMV), then we know
                    156: *     the true residual also must be exactly 0.0.
                    157: *
                    158:          END DO
                    159:       END DO
                    160:       END