01:       SUBROUTINE DLA_LIN_BERR ( N, NZ, NRHS, RES, AYB, BERR )
02: *
03: *     -- LAPACK routine (version 3.2.1)                                 --
04: *     -- Contributed by James Demmel, Deaglan Halligan, Yozo Hida and --
05: *     -- Jason Riedy of Univ. of California Berkeley.                 --
06: *     -- April 2009                                                   --
07: *
08: *     -- LAPACK is a software package provided by Univ. of Tennessee, --
09: *     -- 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 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: *  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: *     RES    (output) DOUBLE PRECISION array, dimension (NRHS)
55: *     The componentwise 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 SUBROUTINE
94: