LAPACK  3.8.0 LAPACK: Linear Algebra PACKage
sget04.f
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1 *> \brief \b SGET04
2 *
3 * =========== DOCUMENTATION ===========
4 *
5 * Online html documentation available at
6 * http://www.netlib.org/lapack/explore-html/
7 *
8 * Definition:
9 * ===========
10 *
11 * SUBROUTINE SGET04( N, NRHS, X, LDX, XACT, LDXACT, RCOND, RESID )
12 *
13 * .. Scalar Arguments ..
14 * INTEGER LDX, LDXACT, N, NRHS
15 * REAL RCOND, RESID
16 * ..
17 * .. Array Arguments ..
18 * REAL X( LDX, * ), XACT( LDXACT, * )
19 * ..
20 *
21 *
22 *> \par Purpose:
23 * =============
24 *>
25 *> \verbatim
26 *>
27 *> SGET04 computes the difference between a computed solution and the
28 *> true solution to a system of linear equations.
29 *>
30 *> RESID = ( norm(X-XACT) * RCOND ) / ( norm(XACT) * EPS ),
31 *> where RCOND is the reciprocal of the condition number and EPS is the
32 *> machine epsilon.
33 *> \endverbatim
34 *
35 * Arguments:
36 * ==========
37 *
38 *> \param[in] N
39 *> \verbatim
40 *> N is INTEGER
41 *> The number of rows of the matrices X and XACT. N >= 0.
42 *> \endverbatim
43 *>
44 *> \param[in] NRHS
45 *> \verbatim
46 *> NRHS is INTEGER
47 *> The number of columns of the matrices X and XACT. NRHS >= 0.
48 *> \endverbatim
49 *>
50 *> \param[in] X
51 *> \verbatim
52 *> X is REAL array, dimension (LDX,NRHS)
53 *> The computed solution vectors. Each vector is stored as a
54 *> column of the matrix X.
55 *> \endverbatim
56 *>
57 *> \param[in] LDX
58 *> \verbatim
59 *> LDX is INTEGER
60 *> The leading dimension of the array X. LDX >= max(1,N).
61 *> \endverbatim
62 *>
63 *> \param[in] XACT
64 *> \verbatim
65 *> XACT is REAL array, dimension( LDX, NRHS )
66 *> The exact solution vectors. Each vector is stored as a
67 *> column of the matrix XACT.
68 *> \endverbatim
69 *>
70 *> \param[in] LDXACT
71 *> \verbatim
72 *> LDXACT is INTEGER
73 *> The leading dimension of the array XACT. LDXACT >= max(1,N).
74 *> \endverbatim
75 *>
76 *> \param[in] RCOND
77 *> \verbatim
78 *> RCOND is REAL
79 *> The reciprocal of the condition number of the coefficient
80 *> matrix in the system of equations.
81 *> \endverbatim
82 *>
83 *> \param[out] RESID
84 *> \verbatim
85 *> RESID is REAL
86 *> The maximum over the NRHS solution vectors of
87 *> ( norm(X-XACT) * RCOND ) / ( norm(XACT) * EPS )
88 *> \endverbatim
89 *
90 * Authors:
91 * ========
92 *
93 *> \author Univ. of Tennessee
94 *> \author Univ. of California Berkeley
95 *> \author Univ. of Colorado Denver
96 *> \author NAG Ltd.
97 *
98 *> \date December 2016
99 *
100 *> \ingroup single_lin
101 *
102 * =====================================================================
103  SUBROUTINE sget04( N, NRHS, X, LDX, XACT, LDXACT, RCOND, RESID )
104 *
105 * -- LAPACK test routine (version 3.7.0) --
106 * -- LAPACK is a software package provided by Univ. of Tennessee, --
107 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
108 * December 2016
109 *
110 * .. Scalar Arguments ..
111  INTEGER LDX, LDXACT, N, NRHS
112  REAL RCOND, RESID
113 * ..
114 * .. Array Arguments ..
115  REAL X( ldx, * ), XACT( ldxact, * )
116 * ..
117 *
118 * =====================================================================
119 *
120 * .. Parameters ..
121  REAL ZERO
122  parameter( zero = 0.0e+0 )
123 * ..
124 * .. Local Scalars ..
125  INTEGER I, IX, J
126  REAL DIFFNM, EPS, XNORM
127 * ..
128 * .. External Functions ..
129  INTEGER ISAMAX
130  REAL SLAMCH
131  EXTERNAL isamax, slamch
132 * ..
133 * .. Intrinsic Functions ..
134  INTRINSIC abs, max
135 * ..
136 * .. Executable Statements ..
137 *
138 * Quick exit if N = 0 or NRHS = 0.
139 *
140  IF( n.LE.0 .OR. nrhs.LE.0 ) THEN
141  resid = zero
142  RETURN
143  END IF
144 *
145 * Exit with RESID = 1/EPS if RCOND is invalid.
146 *
147  eps = slamch( 'Epsilon' )
148  IF( rcond.LT.zero ) THEN
149  resid = 1.0 / eps
150  RETURN
151  END IF
152 *
153 * Compute the maximum of
154 * norm(X - XACT) / ( norm(XACT) * EPS )
155 * over all the vectors X and XACT .
156 *
157  resid = zero
158  DO 20 j = 1, nrhs
159  ix = isamax( n, xact( 1, j ), 1 )
160  xnorm = abs( xact( ix, j ) )
161  diffnm = zero
162  DO 10 i = 1, n
163  diffnm = max( diffnm, abs( x( i, j )-xact( i, j ) ) )
164  10 CONTINUE
165  IF( xnorm.LE.zero ) THEN
166  IF( diffnm.GT.zero )
167  \$ resid = 1.0 / eps
168  ELSE
169  resid = max( resid, ( diffnm / xnorm )*rcond )
170  END IF
171  20 CONTINUE
172  IF( resid*eps.LT.1.0 )
173  \$ resid = resid / eps
174 *
175  RETURN
176 *
177 * End of SGET04
178 *
179  END
subroutine sget04(N, NRHS, X, LDX, XACT, LDXACT, RCOND, RESID)
SGET04
Definition: sget04.f:104