LAPACK 3.12.0 LAPACK: Linear Algebra PACKage
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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*> \ingroup single_lin
99*
100* =====================================================================
101 SUBROUTINE sget04( N, NRHS, X, LDX, XACT, LDXACT, RCOND, RESID )
102*
103* -- LAPACK test routine --
104* -- LAPACK is a software package provided by Univ. of Tennessee, --
105* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
106*
107* .. Scalar Arguments ..
108 INTEGER LDX, LDXACT, N, NRHS
109 REAL RCOND, RESID
110* ..
111* .. Array Arguments ..
112 REAL X( LDX, * ), XACT( LDXACT, * )
113* ..
114*
115* =====================================================================
116*
117* .. Parameters ..
118 REAL ZERO
119 parameter( zero = 0.0e+0 )
120* ..
121* .. Local Scalars ..
122 INTEGER I, IX, J
123 REAL DIFFNM, EPS, XNORM
124* ..
125* .. External Functions ..
126 INTEGER ISAMAX
127 REAL SLAMCH
128 EXTERNAL isamax, slamch
129* ..
130* .. Intrinsic Functions ..
131 INTRINSIC abs, max
132* ..
133* .. Executable Statements ..
134*
135* Quick exit if N = 0 or NRHS = 0.
136*
137 IF( n.LE.0 .OR. nrhs.LE.0 ) THEN
138 resid = zero
139 RETURN
140 END IF
141*
142* Exit with RESID = 1/EPS if RCOND is invalid.
143*
144 eps = slamch( 'Epsilon' )
145 IF( rcond.LT.zero ) THEN
146 resid = 1.0 / eps
147 RETURN
148 END IF
149*
150* Compute the maximum of
151* norm(X - XACT) / ( norm(XACT) * EPS )
152* over all the vectors X and XACT .
153*
154 resid = zero
155 DO 20 j = 1, nrhs
156 ix = isamax( n, xact( 1, j ), 1 )
157 xnorm = abs( xact( ix, j ) )
158 diffnm = zero
159 DO 10 i = 1, n
160 diffnm = max( diffnm, abs( x( i, j )-xact( i, j ) ) )
161 10 CONTINUE
162 IF( xnorm.LE.zero ) THEN
163 IF( diffnm.GT.zero )
164 \$ resid = 1.0 / eps
165 ELSE
166 resid = max( resid, ( diffnm / xnorm )*rcond )
167 END IF
168 20 CONTINUE
169 IF( resid*eps.LT.1.0 )
170 \$ resid = resid / eps
171*
172 RETURN
173*
174* End of SGET04
175*
176 END
subroutine sget04(n, nrhs, x, ldx, xact, ldxact, rcond, resid)
SGET04
Definition sget04.f:102