Annotation of rpl/lapack/lapack/zla_lin_berr.f, revision 1.11
1.8 bertrand 1: *> \brief \b ZLA_LIN_BERR computes a component-wise relative backward error.
1.5 bertrand 2: *
3: * =========== DOCUMENTATION ===========
4: *
5: * Online html documentation available at
6: * http://www.netlib.org/lapack/explore-html/
7: *
8: *> \htmlonly
9: *> Download ZLA_LIN_BERR + dependencies
10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zla_lin_berr.f">
11: *> [TGZ]</a>
12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zla_lin_berr.f">
13: *> [ZIP]</a>
14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zla_lin_berr.f">
15: *> [TXT]</a>
16: *> \endhtmlonly
17: *
18: * Definition:
19: * ===========
20: *
21: * SUBROUTINE ZLA_LIN_BERR ( N, NZ, NRHS, RES, AYB, BERR )
22: *
23: * .. Scalar Arguments ..
24: * INTEGER N, NZ, NRHS
25: * ..
26: * .. Array Arguments ..
27: * DOUBLE PRECISION AYB( N, NRHS ), BERR( NRHS )
28: * COMPLEX*16 RES( N, NRHS )
29: * ..
30: *
31: *
32: *> \par Purpose:
33: * =============
34: *>
35: *> \verbatim
36: *>
37: *> ZLA_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
1.11 ! bertrand 70: *> RES is COMPLEX*16 array, dimension (N,NRHS)
1.5 bertrand 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 DOUBLE PRECISION 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 zla_gerfsx_extended.f).
81: *> \endverbatim
82: *>
83: *> \param[out] BERR
84: *> \verbatim
1.11 ! bertrand 85: *> BERR is DOUBLE PRECISION array, dimension (NRHS)
1.5 bertrand 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: *
1.11 ! bertrand 97: *> \date June 2016
1.5 bertrand 98: *
99: *> \ingroup complex16OTHERcomputational
100: *
101: * =====================================================================
1.1 bertrand 102: SUBROUTINE ZLA_LIN_BERR ( N, NZ, NRHS, RES, AYB, BERR )
103: *
1.11 ! bertrand 104: * -- LAPACK computational routine (version 3.6.1) --
1.5 bertrand 105: * -- LAPACK is a software package provided by Univ. of Tennessee, --
106: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.11 ! bertrand 107: * June 2016
1.1 bertrand 108: *
109: * .. Scalar Arguments ..
110: INTEGER N, NZ, NRHS
111: * ..
112: * .. Array Arguments ..
113: DOUBLE PRECISION AYB( N, NRHS ), BERR( NRHS )
114: COMPLEX*16 RES( N, NRHS )
115: * ..
116: *
117: * =====================================================================
118: *
119: * .. Local Scalars ..
120: DOUBLE PRECISION TMP
121: INTEGER I, J
122: COMPLEX*16 CDUM
123: * ..
124: * .. Intrinsic Functions ..
125: INTRINSIC ABS, REAL, DIMAG, MAX
126: * ..
127: * .. External Functions ..
128: EXTERNAL DLAMCH
129: DOUBLE PRECISION DLAMCH
130: DOUBLE PRECISION SAFE1
131: * ..
132: * .. Statement Functions ..
133: COMPLEX*16 CABS1
134: * ..
135: * .. Statement Function Definitions ..
136: CABS1( CDUM ) = ABS( DBLE( CDUM ) ) + ABS( DIMAG( CDUM ) )
137: * ..
138: * .. Executable Statements ..
139: *
140: * Adding SAFE1 to the numerator guards against spuriously zero
141: * residuals. A similar safeguard is in the CLA_yyAMV routine used
142: * to compute AYB.
143: *
144: SAFE1 = DLAMCH( 'Safe minimum' )
145: SAFE1 = (NZ+1)*SAFE1
146:
147: DO J = 1, NRHS
148: BERR(J) = 0.0D+0
149: DO I = 1, N
150: IF (AYB(I,J) .NE. 0.0D+0) THEN
151: TMP = (SAFE1 + CABS1(RES(I,J)))/AYB(I,J)
152: BERR(J) = MAX( BERR(J), TMP )
153: END IF
154: *
155: * If AYB is exactly 0.0 (and if computed by CLA_yyAMV), then we know
156: * the true residual also must be exactly 0.0.
157: *
158: END DO
159: END DO
160: END
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