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00001       SUBROUTINE SLA_LIN_BERR ( N, NZ, NRHS, RES, AYB, BERR )
00002 *
00003 *     -- LAPACK routine (version 3.2.2)                                 --
00004 *     -- Contributed by James Demmel, Deaglan Halligan, Yozo Hida and --
00005 *     -- Jason Riedy of Univ. of California Berkeley.                 --
00006 *     -- June 2010                                                    --
00007 *
00008 *     -- LAPACK is a software package provided by Univ. of Tennessee, --
00009 *     -- Univ. of California Berkeley and NAG Ltd.                    --
00010 *
00011       IMPLICIT NONE
00012 *     ..
00013 *     .. Scalar Arguments ..
00014       INTEGER            N, NZ, NRHS
00015 *     ..
00016 *     .. Array Arguments ..
00017       REAL               AYB( N, NRHS ), BERR( NRHS )
00018       REAL               RES( N, NRHS )
00019 *     ..
00020 *
00021 *  Purpose
00022 *  =======
00023 *
00024 *     SLA_LIN_BERR computes componentwise relative backward error from
00025 *     the formula
00026 *         max(i) ( abs(R(i)) / ( abs(op(A_s))*abs(Y) + abs(B_s) )(i) )
00027 *     where abs(Z) is the componentwise absolute value of the matrix
00028 *     or vector Z.
00029 *
00030 *  Arguments
00031 *  ==========
00032 *
00033 *     N       (input) INTEGER
00034 *     The number of linear equations, i.e., the order of the
00035 *     matrix A.  N >= 0.
00036 *
00037 *     NZ      (input) INTEGER
00038 *     We add (NZ+1)*SLAMCH( 'Safe minimum' ) to R(i) in the numerator to
00039 *     guard against spuriously zero residuals. Default value is N.
00040 *
00041 *     NRHS    (input) INTEGER
00042 *     The number of right hand sides, i.e., the number of columns
00043 *     of the matrices AYB, RES, and BERR.  NRHS >= 0.
00044 *
00045 *     RES    (input) REAL array, dimension (N,NRHS)
00046 *     The residual matrix, i.e., the matrix R in the relative backward
00047 *     error formula above.
00048 *
00049 *     AYB    (input) REAL array, dimension (N, NRHS)
00050 *     The denominator in the relative backward error formula above, i.e.,
00051 *     the matrix abs(op(A_s))*abs(Y) + abs(B_s). The matrices A, Y, and B
00052 *     are from iterative refinement (see sla_gerfsx_extended.f).
00053 *
00054 *     BERR   (output) REAL array, dimension (NRHS)
00055 *     The componentwise relative backward error from the formula above.
00056 *
00057 *  =====================================================================
00058 *
00059 *     .. Local Scalars ..
00060       REAL               TMP
00061       INTEGER            I, J
00062 *     ..
00063 *     .. Intrinsic Functions ..
00064       INTRINSIC          ABS, MAX
00065 *     ..
00066 *     .. External Functions ..
00067       EXTERNAL           SLAMCH
00068       REAL               SLAMCH
00069       REAL               SAFE1
00070 *     ..
00071 *     .. Executable Statements ..
00072 *
00073 *     Adding SAFE1 to the numerator guards against spuriously zero
00074 *     residuals.  A similar safeguard is in the SLA_yyAMV routine used
00075 *     to compute AYB.
00076 *
00077       SAFE1 = SLAMCH( 'Safe minimum' )
00078       SAFE1 = (NZ+1)*SAFE1
00079
00080       DO J = 1, NRHS
00081          BERR(J) = 0.0
00082          DO I = 1, N
00083             IF (AYB(I,J) .NE. 0.0) THEN
00084                TMP = (SAFE1+ABS(RES(I,J)))/AYB(I,J)
00085                BERR(J) = MAX( BERR(J), TMP )
00086             END IF
00087 *
00088 *     If AYB is exactly 0.0 (and if computed by SLA_yyAMV), then we know
00089 *     the true residual also must be exactly 0.0.
00090 *
00091          END DO
00092       END DO
00093       END