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Annotation of rpl/lapack/lapack/dla_lin_berr.f, revision 1.1

1.1     ! bertrand    1:       SUBROUTINE DLA_LIN_BERR ( N, NZ, NRHS, RES, AYB, BERR )
        !             2: *
        !             3: *     -- LAPACK routine (version 3.2.2)                                 --
        !             4: *     -- Contributed by James Demmel, Deaglan Halligan, Yozo Hida and --
        !             5: *     -- Jason Riedy of Univ. of California Berkeley.                 --
        !             6: *     -- June 2010                                                    --
        !             7: *
        !             8: *     -- LAPACK is a software package provided by Univ. of Tennessee, --
        !             9: *     -- Univ. of California Berkeley and NAG Ltd.                    --
        !            10: *
        !            11:       IMPLICIT NONE
        !            12: *     ..
        !            13: *     .. Scalar Arguments ..
        !            14:       INTEGER            N, NZ, NRHS
        !            15: *     ..
        !            16: *     .. Array Arguments ..
        !            17:       DOUBLE PRECISION   AYB( N, NRHS ), BERR( NRHS )
        !            18:       DOUBLE PRECISION   RES( N, NRHS )
        !            19: *     ..
        !            20: *
        !            21: *  Purpose
        !            22: *  =======
        !            23: *
        !            24: *     DLA_LIN_BERR computes component-wise relative backward error from
        !            25: *     the formula
        !            26: *         max(i) ( abs(R(i)) / ( abs(op(A_s))*abs(Y) + abs(B_s) )(i) )
        !            27: *     where abs(Z) is the component-wise absolute value of the matrix
        !            28: *     or vector Z.
        !            29: *
        !            30: *  Arguments
        !            31: *  ==========
        !            32: *
        !            33: *     N       (input) INTEGER
        !            34: *     The number of linear equations, i.e., the order of the
        !            35: *     matrix A.  N >= 0.
        !            36: *
        !            37: *     NZ      (input) INTEGER
        !            38: *     We add (NZ+1)*SLAMCH( 'Safe minimum' ) to R(i) in the numerator to
        !            39: *     guard against spuriously zero residuals. Default value is N.
        !            40: *
        !            41: *     NRHS    (input) INTEGER
        !            42: *     The number of right hand sides, i.e., the number of columns
        !            43: *     of the matrices AYB, RES, and BERR.  NRHS >= 0.
        !            44: *
        !            45: *     RES     (input) DOUBLE PRECISION array, dimension (N,NRHS)
        !            46: *     The residual matrix, i.e., the matrix R in the relative backward
        !            47: *     error formula above.
        !            48: *
        !            49: *     AYB     (input) DOUBLE PRECISION array, dimension (N, NRHS)
        !            50: *     The denominator in the relative backward error formula above, i.e.,
        !            51: *     the matrix abs(op(A_s))*abs(Y) + abs(B_s). The matrices A, Y, and B
        !            52: *     are from iterative refinement (see dla_gerfsx_extended.f).
        !            53: *     
        !            54: *     BERR    (output) DOUBLE PRECISION array, dimension (NRHS)
        !            55: *     The component-wise relative backward error from the formula above.
        !            56: *
        !            57: *  =====================================================================
        !            58: *
        !            59: *     .. Local Scalars ..
        !            60:       DOUBLE PRECISION   TMP
        !            61:       INTEGER            I, J
        !            62: *     ..
        !            63: *     .. Intrinsic Functions ..
        !            64:       INTRINSIC          ABS, MAX
        !            65: *     ..
        !            66: *     .. External Functions ..
        !            67:       EXTERNAL           DLAMCH
        !            68:       DOUBLE PRECISION   DLAMCH
        !            69:       DOUBLE PRECISION   SAFE1
        !            70: *     ..
        !            71: *     .. Executable Statements ..
        !            72: *
        !            73: *     Adding SAFE1 to the numerator guards against spuriously zero
        !            74: *     residuals.  A similar safeguard is in the SLA_yyAMV routine used
        !            75: *     to compute AYB.
        !            76: *
        !            77:       SAFE1 = DLAMCH( 'Safe minimum' )
        !            78:       SAFE1 = (NZ+1)*SAFE1
        !            79: 
        !            80:       DO J = 1, NRHS
        !            81:          BERR(J) = 0.0D+0
        !            82:          DO I = 1, N
        !            83:             IF (AYB(I,J) .NE. 0.0D+0) THEN
        !            84:                TMP = (SAFE1+ABS(RES(I,J)))/AYB(I,J)
        !            85:                BERR(J) = MAX( BERR(J), TMP )
        !            86:             END IF
        !            87: *
        !            88: *     If AYB is exactly 0.0 (and if computed by SLA_yyAMV), then we know
        !            89: *     the true residual also must be exactly 0.0.
        !            90: *
        !            91:          END DO
        !            92:       END DO
        !            93:       END