LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
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cla_lin_berr.f
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1*> \brief \b CLA_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*> \htmlonly
10*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/cla_lin_berr.f">
11*> [TGZ]</a>
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13*> [ZIP]</a>
14*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/cla_lin_berr.f">
15*> [TXT]</a>
16*> \endhtmlonly
17*
18* Definition:
19* ===========
20*
21* SUBROUTINE CLA_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* COMPLEX RES( N, NRHS )
29* ..
30*
31*
32*> \par Purpose:
33* =============
34*>
35*> \verbatim
36*>
37*> CLA_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 COMPLEX 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 cla_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 complexOTHERcomputational
98*
99* =====================================================================
100 SUBROUTINE cla_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 COMPLEX RES( N, NRHS )
112* ..
113*
114* =====================================================================
115*
116* .. Local Scalars ..
117 REAL TMP
118 INTEGER I, J
119 COMPLEX CDUM
120* ..
121* .. Intrinsic Functions ..
122 INTRINSIC abs, real, aimag, max
123* ..
124* .. External Functions ..
125 EXTERNAL slamch
126 REAL SLAMCH
127 REAL SAFE1
128* ..
129* .. Statement Functions ..
130 COMPLEX CABS1
131* ..
132* .. Statement Function Definitions ..
133 cabs1( cdum ) = abs( real( cdum ) ) + abs( aimag( cdum ) )
134* ..
135* .. Executable Statements ..
136*
137* Adding SAFE1 to the numerator guards against spuriously zero
138* residuals. A similar safeguard is in the CLA_yyAMV routine used
139* to compute AYB.
140*
141 safe1 = slamch( 'Safe minimum' )
142 safe1 = (nz+1)*safe1
143
144 DO j = 1, nrhs
145 berr(j) = 0.0
146 DO i = 1, n
147 IF (ayb(i,j) .NE. 0.0) THEN
148 tmp = (safe1 + cabs1(res(i,j)))/ayb(i,j)
149 berr(j) = max( berr(j), tmp )
150 END IF
151*
152* If AYB is exactly 0.0 (and if computed by CLA_yyAMV), then we know
153* the true residual also must be exactly 0.0.
154*
155 END DO
156 END DO
157*
158* End of CLA_LIN_BERR
159*
160 END
subroutine cla_lin_berr(N, NZ, NRHS, RES, AYB, BERR)
CLA_LIN_BERR computes a component-wise relative backward error.
Definition: cla_lin_berr.f:101
real function slamch(CMACH)
SLAMCH
Definition: slamch.f:68