Annotation of rpl/lapack/lapack/dla_lin_berr.f, revision 1.15

1.8       bertrand    1: *> \brief \b DLA_LIN_BERR computes a component-wise relative backward error.
1.5       bertrand    2: *
                      3: *  =========== DOCUMENTATION ===========
                      4: *
1.12      bertrand    5: * Online html documentation available at
                      6: *            http://www.netlib.org/lapack/explore-html/
1.5       bertrand    7: *
                      8: *> \htmlonly
1.12      bertrand    9: *> Download DLA_LIN_BERR + dependencies
                     10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dla_lin_berr.f">
                     11: *> [TGZ]</a>
                     12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dla_lin_berr.f">
                     13: *> [ZIP]</a>
                     14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dla_lin_berr.f">
1.5       bertrand   15: *> [TXT]</a>
1.12      bertrand   16: *> \endhtmlonly
1.5       bertrand   17: *
                     18: *  Definition:
                     19: *  ===========
                     20: *
1.15    ! bertrand   21: *       SUBROUTINE DLA_LIN_BERR( N, NZ, NRHS, RES, AYB, BERR )
1.12      bertrand   22: *
1.5       bertrand   23: *       .. Scalar Arguments ..
                     24: *       INTEGER            N, NZ, NRHS
                     25: *       ..
                     26: *       .. Array Arguments ..
                     27: *       DOUBLE PRECISION   AYB( N, NRHS ), BERR( NRHS )
                     28: *       DOUBLE PRECISION   RES( N, NRHS )
                     29: *       ..
1.12      bertrand   30: *
1.5       bertrand   31: *
                     32: *> \par Purpose:
                     33: *  =============
                     34: *>
                     35: *> \verbatim
                     36: *>
                     37: *>    DLA_LIN_BERR computes component-wise 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 component-wise 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 dla_gerfsx_extended.f).
                     81: *> \endverbatim
1.12      bertrand   82: *>
1.5       bertrand   83: *> \param[out] BERR
                     84: *> \verbatim
                     85: *>          BERR is DOUBLE PRECISION array, dimension (NRHS)
                     86: *>     The component-wise relative backward error from the formula above.
                     87: *> \endverbatim
                     88: *
                     89: *  Authors:
                     90: *  ========
                     91: *
1.12      bertrand   92: *> \author Univ. of Tennessee
                     93: *> \author Univ. of California Berkeley
                     94: *> \author Univ. of Colorado Denver
                     95: *> \author NAG Ltd.
1.5       bertrand   96: *
                     97: *> \ingroup doubleOTHERcomputational
                     98: *
                     99: *  =====================================================================
1.1       bertrand  100:       SUBROUTINE DLA_LIN_BERR ( N, NZ, NRHS, RES, AYB, BERR )
                    101: *
1.15    ! bertrand  102: *  -- LAPACK computational routine --
1.5       bertrand  103: *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
                    104: *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.1       bertrand  105: *
                    106: *     .. Scalar Arguments ..
                    107:       INTEGER            N, NZ, NRHS
                    108: *     ..
                    109: *     .. Array Arguments ..
                    110:       DOUBLE PRECISION   AYB( N, NRHS ), BERR( NRHS )
                    111:       DOUBLE PRECISION   RES( N, NRHS )
                    112: *     ..
                    113: *
                    114: *  =====================================================================
                    115: *
                    116: *     .. Local Scalars ..
                    117:       DOUBLE PRECISION   TMP
                    118:       INTEGER            I, J
                    119: *     ..
                    120: *     .. Intrinsic Functions ..
                    121:       INTRINSIC          ABS, MAX
                    122: *     ..
                    123: *     .. External Functions ..
                    124:       EXTERNAL           DLAMCH
                    125:       DOUBLE PRECISION   DLAMCH
                    126:       DOUBLE PRECISION   SAFE1
                    127: *     ..
                    128: *     .. Executable Statements ..
                    129: *
                    130: *     Adding SAFE1 to the numerator guards against spuriously zero
                    131: *     residuals.  A similar safeguard is in the SLA_yyAMV routine used
                    132: *     to compute AYB.
                    133: *
                    134:       SAFE1 = DLAMCH( 'Safe minimum' )
                    135:       SAFE1 = (NZ+1)*SAFE1
                    136: 
                    137:       DO J = 1, NRHS
                    138:          BERR(J) = 0.0D+0
                    139:          DO I = 1, N
                    140:             IF (AYB(I,J) .NE. 0.0D+0) THEN
                    141:                TMP = (SAFE1+ABS(RES(I,J)))/AYB(I,J)
                    142:                BERR(J) = MAX( BERR(J), TMP )
                    143:             END IF
                    144: *
                    145: *     If AYB is exactly 0.0 (and if computed by SLA_yyAMV), then we know
                    146: *     the true residual also must be exactly 0.0.
                    147: *
                    148:          END DO
                    149:       END DO
1.15    ! bertrand  150: *
        !           151: *     End of DLA_LIN_BERR
        !           152: *
1.1       bertrand  153:       END

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