Annotation of rpl/lapack/lapack/zla_lin_berr.f, revision 1.16
1.8 bertrand 1: *> \brief \b ZLA_LIN_BERR computes a component-wise relative backward error.
1.5 bertrand 2: *
3: * =========== DOCUMENTATION ===========
4: *
1.13 bertrand 5: * Online html documentation available at
6: * http://www.netlib.org/lapack/explore-html/
1.5 bertrand 7: *
8: *> \htmlonly
1.13 bertrand 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">
1.5 bertrand 15: *> [TXT]</a>
1.13 bertrand 16: *> \endhtmlonly
1.5 bertrand 17: *
18: * Definition:
19: * ===========
20: *
1.16 ! bertrand 21: * SUBROUTINE ZLA_LIN_BERR( N, NZ, NRHS, RES, AYB, BERR )
1.13 bertrand 22: *
1.5 bertrand 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: * ..
1.13 bertrand 30: *
1.5 bertrand 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
1.13 bertrand 82: *>
1.5 bertrand 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: *
1.13 bertrand 92: *> \author Univ. of Tennessee
93: *> \author Univ. of California Berkeley
94: *> \author Univ. of Colorado Denver
95: *> \author NAG Ltd.
1.5 bertrand 96: *
97: *> \ingroup complex16OTHERcomputational
98: *
99: * =====================================================================
1.16 ! bertrand 100: SUBROUTINE ZLA_LIN_BERR( N, NZ, NRHS, RES, AYB, BERR )
1.1 bertrand 101: *
1.16 ! bertrand 102: * -- LAPACK computational routine --
1.5 bertrand 103: * -- LAPACK is a software package provided by Univ. of Tennessee, --
104: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.1 bertrand 105: *
106: * .. Scalar Arguments ..
107: INTEGER N, NZ, NRHS
108: * ..
109: * .. Array Arguments ..
110: DOUBLE PRECISION AYB( N, NRHS ), BERR( NRHS )
111: COMPLEX*16 RES( N, NRHS )
112: * ..
113: *
114: * =====================================================================
115: *
116: * .. Local Scalars ..
117: DOUBLE PRECISION TMP
118: INTEGER I, J
119: COMPLEX*16 CDUM
120: * ..
121: * .. Intrinsic Functions ..
122: INTRINSIC ABS, REAL, DIMAG, MAX
123: * ..
124: * .. External Functions ..
125: EXTERNAL DLAMCH
126: DOUBLE PRECISION DLAMCH
127: DOUBLE PRECISION SAFE1
128: * ..
129: * .. Statement Functions ..
130: COMPLEX*16 CABS1
131: * ..
132: * .. Statement Function Definitions ..
133: CABS1( CDUM ) = ABS( DBLE( CDUM ) ) + ABS( DIMAG( 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 = DLAMCH( 'Safe minimum' )
142: SAFE1 = (NZ+1)*SAFE1
143:
144: DO J = 1, NRHS
145: BERR(J) = 0.0D+0
146: DO I = 1, N
147: IF (AYB(I,J) .NE. 0.0D+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
1.16 ! bertrand 157: *
! 158: * End of ZLA_LIN_BERR
! 159: *
1.1 bertrand 160: END
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