LAPACK  3.10.1 LAPACK: Linear Algebra PACKage
sla_lin_berr.f
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1 *> \brief \b SLA_LIN_BERR computes a component-wise relative backward error.
2 *
3 * =========== DOCUMENTATION ===========
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17 *
18 * Definition:
19 * ===========
20 *
21 * SUBROUTINE SLA_LIN_BERR( N, NZ, NRHS, RES, AYB, BERR )
22 *
23 * .. Scalar Arguments ..
24 * INTEGER N, NZ, NRHS
25 * ..
26 * .. Array Arguments ..
27 * REAL AYB( N, NRHS ), BERR( NRHS )
28 * REAL RES( N, NRHS )
29 * ..
30 *
31 *
32 *> \par Purpose:
33 * =============
34 *>
35 *> \verbatim
36 *>
37 *> SLA_LIN_BERR computes componentwise 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 componentwise 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 REAL 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 REAL 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 sla_gerfsx_extended.f).
81 *> \endverbatim
82 *>
83 *> \param[out] BERR
84 *> \verbatim
85 *> BERR is REAL array, dimension (NRHS)
86 *> The componentwise relative backward error from the formula above.
87 *> \endverbatim
88 *
89 * Authors:
90 * ========
91 *
92 *> \author Univ. of Tennessee
93 *> \author Univ. of California Berkeley
94 *> \author Univ. of Colorado Denver
95 *> \author NAG Ltd.
96 *
97 *> \ingroup realOTHERcomputational
98 *
99 * =====================================================================
100  SUBROUTINE sla_lin_berr( N, NZ, NRHS, RES, AYB, BERR )
101 *
102 * -- LAPACK computational routine --
103 * -- LAPACK is a software package provided by Univ. of Tennessee, --
104 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
105 *
106 * .. Scalar Arguments ..
107  INTEGER N, NZ, NRHS
108 * ..
109 * .. Array Arguments ..
110  REAL AYB( N, NRHS ), BERR( NRHS )
111  REAL RES( N, NRHS )
112 * ..
113 *
114 * =====================================================================
115 *
116 * .. Local Scalars ..
117  REAL TMP
118  INTEGER I, J
119 * ..
120 * .. Intrinsic Functions ..
121  INTRINSIC abs, max
122 * ..
123 * .. External Functions ..
124  EXTERNAL slamch
125  REAL SLAMCH
126  REAL 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 = slamch( 'Safe minimum' )
135  safe1 = (nz+1)*safe1
136
137  DO j = 1, nrhs
138  berr(j) = 0.0
139  DO i = 1, n
140  IF (ayb(i,j) .NE. 0.0) 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
150 *
151 * End of SLA_LIN_BERR
152 *
153  END
subroutine sla_lin_berr(N, NZ, NRHS, RES, AYB, BERR)
SLA_LIN_BERR computes a component-wise relative backward error.
Definition: sla_lin_berr.f:101
real function slamch(CMACH)
SLAMCH
Definition: slamch.f:68