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

1.1     ! bertrand    1:       SUBROUTINE ZLA_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:       COMPLEX*16         RES( N, NRHS )
        !            19: *     ..
        !            20: *
        !            21: *  Purpose
        !            22: *  =======
        !            23: *
        !            24: *     ZLA_LIN_BERR computes componentwise 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 componentwise absolute value of the matrix
        !            28: *     or vector Z.
        !            29: *
        !            30: *     N       (input) INTEGER
        !            31: *     The number of linear equations, i.e., the order of the
        !            32: *     matrix A.  N >= 0.
        !            33: *
        !            34: *     NZ      (input) INTEGER
        !            35: *     We add (NZ+1)*SLAMCH( 'Safe minimum' ) to R(i) in the numerator to
        !            36: *     guard against spuriously zero residuals. Default value is N.
        !            37: *
        !            38: *     NRHS    (input) INTEGER
        !            39: *     The number of right hand sides, i.e., the number of columns
        !            40: *     of the matrices AYB, RES, and BERR.  NRHS >= 0.
        !            41: *
        !            42: *     RES    (input) DOUBLE PRECISION array, dimension (N,NRHS)
        !            43: *     The residual matrix, i.e., the matrix R in the relative backward
        !            44: *     error formula above.
        !            45: *
        !            46: *     AYB    (input) DOUBLE PRECISION array, dimension (N, NRHS)
        !            47: *     The denominator in the relative backward error formula above, i.e.,
        !            48: *     the matrix abs(op(A_s))*abs(Y) + abs(B_s). The matrices A, Y, and B
        !            49: *     are from iterative refinement (see zla_gerfsx_extended.f).
        !            50: *     
        !            51: *     BERR   (output) COMPLEX*16 array, dimension (NRHS)
        !            52: *     The componentwise relative backward error from the formula above.
        !            53: *
        !            54: *  =====================================================================
        !            55: *
        !            56: *     .. Local Scalars ..
        !            57:       DOUBLE PRECISION   TMP
        !            58:       INTEGER            I, J
        !            59:       COMPLEX*16         CDUM
        !            60: *     ..
        !            61: *     .. Intrinsic Functions ..
        !            62:       INTRINSIC          ABS, REAL, DIMAG, MAX
        !            63: *     ..
        !            64: *     .. External Functions ..
        !            65:       EXTERNAL           DLAMCH
        !            66:       DOUBLE PRECISION   DLAMCH
        !            67:       DOUBLE PRECISION   SAFE1
        !            68: *     ..
        !            69: *     .. Statement Functions ..
        !            70:       COMPLEX*16         CABS1
        !            71: *     ..
        !            72: *     .. Statement Function Definitions ..
        !            73:       CABS1( CDUM ) = ABS( DBLE( CDUM ) ) + ABS( DIMAG( CDUM ) )
        !            74: *     ..
        !            75: *     .. Executable Statements ..
        !            76: *
        !            77: *     Adding SAFE1 to the numerator guards against spuriously zero
        !            78: *     residuals.  A similar safeguard is in the CLA_yyAMV routine used
        !            79: *     to compute AYB.
        !            80: *
        !            81:       SAFE1 = DLAMCH( 'Safe minimum' )
        !            82:       SAFE1 = (NZ+1)*SAFE1
        !            83: 
        !            84:       DO J = 1, NRHS
        !            85:          BERR(J) = 0.0D+0
        !            86:          DO I = 1, N
        !            87:             IF (AYB(I,J) .NE. 0.0D+0) THEN
        !            88:                TMP = (SAFE1 + CABS1(RES(I,J)))/AYB(I,J)
        !            89:                BERR(J) = MAX( BERR(J), TMP )
        !            90:             END IF
        !            91: *
        !            92: *     If AYB is exactly 0.0 (and if computed by CLA_yyAMV), then we know
        !            93: *     the true residual also must be exactly 0.0.
        !            94: *
        !            95:          END DO
        !            96:       END DO
        !            97:       END