LAPACK 3.12.1
LAPACK: Linear Algebra PACKage
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zla_lin_berr.f
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1*> \brief \b ZLA_LIN_BERR computes a component-wise relative backward error.
2*
3* =========== DOCUMENTATION ===========
4*
5* Online html documentation available at
6* http://www.netlib.org/lapack/explore-html/
7*
8*> Download ZLA_LIN_BERR + dependencies
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10*> [TGZ]</a>
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12*> [ZIP]</a>
13*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zla_lin_berr.f">
14*> [TXT]</a>
15*
16* Definition:
17* ===========
18*
19* SUBROUTINE ZLA_LIN_BERR( N, NZ, NRHS, RES, AYB, BERR )
20*
21* .. Scalar Arguments ..
22* INTEGER N, NZ, NRHS
23* ..
24* .. Array Arguments ..
25* DOUBLE PRECISION AYB( N, NRHS ), BERR( NRHS )
26* COMPLEX*16 RES( N, NRHS )
27* ..
28*
29*
30*> \par Purpose:
31* =============
32*>
33*> \verbatim
34*>
35*> ZLA_LIN_BERR computes componentwise relative backward error from
36*> the formula
37*> max(i) ( abs(R(i)) / ( abs(op(A_s))*abs(Y) + abs(B_s) )(i) )
38*> where abs(Z) is the componentwise absolute value of the matrix
39*> or vector Z.
40*> \endverbatim
41*
42* Arguments:
43* ==========
44*
45*> \param[in] N
46*> \verbatim
47*> N is INTEGER
48*> The number of linear equations, i.e., the order of the
49*> matrix A. N >= 0.
50*> \endverbatim
51*>
52*> \param[in] NZ
53*> \verbatim
54*> NZ is INTEGER
55*> We add (NZ+1)*SLAMCH( 'Safe minimum' ) to R(i) in the numerator to
56*> guard against spuriously zero residuals. Default value is N.
57*> \endverbatim
58*>
59*> \param[in] NRHS
60*> \verbatim
61*> NRHS is INTEGER
62*> The number of right hand sides, i.e., the number of columns
63*> of the matrices AYB, RES, and BERR. NRHS >= 0.
64*> \endverbatim
65*>
66*> \param[in] RES
67*> \verbatim
68*> RES is COMPLEX*16 array, dimension (N,NRHS)
69*> The residual matrix, i.e., the matrix R in the relative backward
70*> error formula above.
71*> \endverbatim
72*>
73*> \param[in] AYB
74*> \verbatim
75*> AYB is DOUBLE PRECISION array, dimension (N, NRHS)
76*> The denominator in the relative backward error formula above, i.e.,
77*> the matrix abs(op(A_s))*abs(Y) + abs(B_s). The matrices A, Y, and B
78*> are from iterative refinement (see zla_gerfsx_extended.f).
79*> \endverbatim
80*>
81*> \param[out] BERR
82*> \verbatim
83*> BERR is DOUBLE PRECISION array, dimension (NRHS)
84*> The componentwise relative backward error from the formula above.
85*> \endverbatim
86*
87* Authors:
88* ========
89*
90*> \author Univ. of Tennessee
91*> \author Univ. of California Berkeley
92*> \author Univ. of Colorado Denver
93*> \author NAG Ltd.
94*
95*> \ingroup la_lin_berr
96*
97* =====================================================================
98 SUBROUTINE zla_lin_berr( N, NZ, NRHS, RES, AYB, BERR )
99*
100* -- LAPACK computational routine --
101* -- LAPACK is a software package provided by Univ. of Tennessee, --
102* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
103*
104* .. Scalar Arguments ..
105 INTEGER N, NZ, NRHS
106* ..
107* .. Array Arguments ..
108 DOUBLE PRECISION AYB( N, NRHS ), BERR( NRHS )
109 COMPLEX*16 RES( N, NRHS )
110* ..
111*
112* =====================================================================
113*
114* .. Local Scalars ..
115 DOUBLE PRECISION TMP
116 INTEGER I, J
117 COMPLEX*16 CDUM
118* ..
119* .. Intrinsic Functions ..
120 INTRINSIC abs, real, dimag, max
121* ..
122* .. External Functions ..
123 EXTERNAL dlamch
124 DOUBLE PRECISION DLAMCH
125 DOUBLE PRECISION SAFE1
126* ..
127* .. Statement Functions ..
128 COMPLEX*16 CABS1
129* ..
130* .. Statement Function Definitions ..
131 cabs1( cdum ) = abs( dble( cdum ) ) + abs( dimag( cdum ) )
132* ..
133* .. Executable Statements ..
134*
135* Adding SAFE1 to the numerator guards against spuriously zero
136* residuals. A similar safeguard is in the CLA_yyAMV routine used
137* to compute AYB.
138*
139 safe1 = dlamch( 'Safe minimum' )
140 safe1 = (nz+1)*safe1
141
142 DO j = 1, nrhs
143 berr(j) = 0.0d+0
144 DO i = 1, n
145 IF (ayb(i,j) .NE. 0.0d+0) THEN
146 tmp = (safe1 + cabs1(res(i,j)))/ayb(i,j)
147 berr(j) = max( berr(j), tmp )
148 END IF
149*
150* If AYB is exactly 0.0 (and if computed by CLA_yyAMV), then we know
151* the true residual also must be exactly 0.0.
152*
153 END DO
154 END DO
155*
156* End of ZLA_LIN_BERR
157*
158 END
subroutine zla_lin_berr(n, nz, nrhs, res, ayb, berr)
ZLA_LIN_BERR computes a component-wise relative backward error.
double precision function dlamch(cmach)
DLAMCH
Definition dlamch.f:69