1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
|
*> \brief \b DGET02
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition:
* ===========
*
* SUBROUTINE DGET02( TRANS, M, N, NRHS, A, LDA, X, LDX, B, LDB,
* RWORK, RESID )
*
* .. Scalar Arguments ..
* CHARACTER TRANS
* INTEGER LDA, LDB, LDX, M, N, NRHS
* DOUBLE PRECISION RESID
* ..
* .. Array Arguments ..
* DOUBLE PRECISION A( LDA, * ), B( LDB, * ), RWORK( * ),
* $ X( LDX, * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> DGET02 computes the residual for a solution of a system of linear
*> equations A*x = b or A'*x = b:
*> RESID = norm(B - A*X) / ( norm(A) * norm(X) * EPS ),
*> where EPS is the machine epsilon.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] TRANS
*> \verbatim
*> TRANS is CHARACTER*1
*> Specifies the form of the system of equations:
*> = 'N': A *x = b
*> = 'T': A'*x = b, where A' is the transpose of A
*> = 'C': A'*x = b, where A' is the transpose of A
*> \endverbatim
*>
*> \param[in] M
*> \verbatim
*> M is INTEGER
*> The number of rows of the matrix A. M >= 0.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> The number of columns of the matrix A. N >= 0.
*> \endverbatim
*>
*> \param[in] NRHS
*> \verbatim
*> NRHS is INTEGER
*> The number of columns of B, the matrix of right hand sides.
*> NRHS >= 0.
*> \endverbatim
*>
*> \param[in] A
*> \verbatim
*> A is DOUBLE PRECISION array, dimension (LDA,N)
*> The original M x N matrix A.
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*> LDA is INTEGER
*> The leading dimension of the array A. LDA >= max(1,M).
*> \endverbatim
*>
*> \param[in] X
*> \verbatim
*> X is DOUBLE PRECISION array, dimension (LDX,NRHS)
*> The computed solution vectors for the system of linear
*> equations.
*> \endverbatim
*>
*> \param[in] LDX
*> \verbatim
*> LDX is INTEGER
*> The leading dimension of the array X. If TRANS = 'N',
*> LDX >= max(1,N); if TRANS = 'T' or 'C', LDX >= max(1,M).
*> \endverbatim
*>
*> \param[in,out] B
*> \verbatim
*> B is DOUBLE PRECISION array, dimension (LDB,NRHS)
*> On entry, the right hand side vectors for the system of
*> linear equations.
*> On exit, B is overwritten with the difference B - A*X.
*> \endverbatim
*>
*> \param[in] LDB
*> \verbatim
*> LDB is INTEGER
*> The leading dimension of the array B. IF TRANS = 'N',
*> LDB >= max(1,M); if TRANS = 'T' or 'C', LDB >= max(1,N).
*> \endverbatim
*>
*> \param[out] RWORK
*> \verbatim
*> RWORK is DOUBLE PRECISION array, dimension (M)
*> \endverbatim
*>
*> \param[out] RESID
*> \verbatim
*> RESID is DOUBLE PRECISION
*> The maximum over the number of right hand sides of
*> norm(B - A*X) / ( norm(A) * norm(X) * EPS ).
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date June 2017
*
*> \ingroup double_eig
*
* =====================================================================
SUBROUTINE DGET02( TRANS, M, N, NRHS, A, LDA, X, LDX, B, LDB,
$ RWORK, RESID )
*
* -- LAPACK test routine (version 3.7.1) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
* June 2017
*
* .. Scalar Arguments ..
CHARACTER TRANS
INTEGER LDA, LDB, LDX, M, N, NRHS
DOUBLE PRECISION RESID
* ..
* .. Array Arguments ..
DOUBLE PRECISION A( LDA, * ), B( LDB, * ), RWORK( * ),
$ X( LDX, * )
* ..
*
* =====================================================================
*
* .. Parameters ..
DOUBLE PRECISION ZERO, ONE
PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 )
* ..
* .. Local Scalars ..
INTEGER J, N1, N2
DOUBLE PRECISION ANORM, BNORM, EPS, XNORM
* ..
* .. External Functions ..
LOGICAL LSAME
DOUBLE PRECISION DASUM, DLAMCH, DLANGE
EXTERNAL LSAME, DASUM, DLAMCH, DLANGE
* ..
* .. External Subroutines ..
EXTERNAL DGEMM
* ..
* .. Intrinsic Functions ..
INTRINSIC MAX
* ..
* .. Executable Statements ..
*
* Quick exit if M = 0 or N = 0 or NRHS = 0
*
IF( M.LE.0 .OR. N.LE.0 .OR. NRHS.EQ.0 ) THEN
RESID = ZERO
RETURN
END IF
*
IF( LSAME( TRANS, 'T' ) .OR. LSAME( TRANS, 'C' ) ) THEN
N1 = N
N2 = M
ELSE
N1 = M
N2 = N
END IF
*
* Exit with RESID = 1/EPS if ANORM = 0.
*
EPS = DLAMCH( 'Epsilon' )
ANORM = DLANGE( '1', M, N, A, LDA, RWORK )
IF( ANORM.LE.ZERO ) THEN
RESID = ONE / EPS
RETURN
END IF
*
* Compute B - A*X (or B - A'*X ) and store in B.
*
CALL DGEMM( TRANS, 'No transpose', N1, NRHS, N2, -ONE, A, LDA, X,
$ LDX, ONE, B, LDB )
*
* Compute the maximum over the number of right hand sides of
* norm(B - A*X) / ( norm(A) * norm(X) * EPS ) .
*
RESID = ZERO
DO 10 J = 1, NRHS
BNORM = DASUM( N1, B( 1, J ), 1 )
XNORM = DASUM( N2, X( 1, J ), 1 )
IF( XNORM.LE.ZERO ) THEN
RESID = ONE / EPS
ELSE
RESID = MAX( RESID, ( ( BNORM / ANORM ) / XNORM ) / EPS )
END IF
10 CONTINUE
*
RETURN
*
* End of DGET02
*
END
|
