LAPACK  3.10.1
LAPACK: Linear Algebra PACKage
dget02.f
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1 *> \brief \b DGET02
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 DGET02( TRANS, M, N, NRHS, A, LDA, X, LDX, B, LDB,
12 * RWORK, RESID )
13 *
14 * .. Scalar Arguments ..
15 * CHARACTER TRANS
16 * INTEGER LDA, LDB, LDX, M, N, NRHS
17 * DOUBLE PRECISION RESID
18 * ..
19 * .. Array Arguments ..
20 * DOUBLE PRECISION A( LDA, * ), B( LDB, * ), RWORK( * ),
21 * $ X( LDX, * )
22 * ..
23 *
24 *
25 *> \par Purpose:
26 * =============
27 *>
28 *> \verbatim
29 *>
30 *> DGET02 computes the residual for a solution of a system of linear
31 *> equations op(A)*X = B:
32 *> RESID = norm(B - op(A)*X) / ( norm(op(A)) * norm(X) * EPS ),
33 *> where op(A) = A or A**T, depending on TRANS, and EPS is the
34 *> machine epsilon.
35 *> The norm used is the 1-norm.
36 *> \endverbatim
37 *
38 * Arguments:
39 * ==========
40 *
41 *> \param[in] TRANS
42 *> \verbatim
43 *> TRANS is CHARACTER*1
44 *> Specifies the form of the system of equations:
45 *> = 'N': A * X = B (No transpose)
46 *> = 'T': A**T * X = B (Transpose)
47 *> = 'C': A**H * X = B (Conjugate transpose = Transpose)
48 *> \endverbatim
49 *>
50 *> \param[in] M
51 *> \verbatim
52 *> M is INTEGER
53 *> The number of rows of the matrix A. M >= 0.
54 *> \endverbatim
55 *>
56 *> \param[in] N
57 *> \verbatim
58 *> N is INTEGER
59 *> The number of columns of the matrix A. N >= 0.
60 *> \endverbatim
61 *>
62 *> \param[in] NRHS
63 *> \verbatim
64 *> NRHS is INTEGER
65 *> The number of columns of B, the matrix of right hand sides.
66 *> NRHS >= 0.
67 *> \endverbatim
68 *>
69 *> \param[in] A
70 *> \verbatim
71 *> A is DOUBLE PRECISION array, dimension (LDA,N)
72 *> The original M x N matrix A.
73 *> \endverbatim
74 *>
75 *> \param[in] LDA
76 *> \verbatim
77 *> LDA is INTEGER
78 *> The leading dimension of the array A. LDA >= max(1,M).
79 *> \endverbatim
80 *>
81 *> \param[in] X
82 *> \verbatim
83 *> X is DOUBLE PRECISION array, dimension (LDX,NRHS)
84 *> The computed solution vectors for the system of linear
85 *> equations.
86 *> \endverbatim
87 *>
88 *> \param[in] LDX
89 *> \verbatim
90 *> LDX is INTEGER
91 *> The leading dimension of the array X. If TRANS = 'N',
92 *> LDX >= max(1,N); if TRANS = 'T' or 'C', LDX >= max(1,M).
93 *> \endverbatim
94 *>
95 *> \param[in,out] B
96 *> \verbatim
97 *> B is DOUBLE PRECISION array, dimension (LDB,NRHS)
98 *> On entry, the right hand side vectors for the system of
99 *> linear equations.
100 *> On exit, B is overwritten with the difference B - A*X.
101 *> \endverbatim
102 *>
103 *> \param[in] LDB
104 *> \verbatim
105 *> LDB is INTEGER
106 *> The leading dimension of the array B. IF TRANS = 'N',
107 *> LDB >= max(1,M); if TRANS = 'T' or 'C', LDB >= max(1,N).
108 *> \endverbatim
109 *>
110 *> \param[out] RWORK
111 *> \verbatim
112 *> RWORK is DOUBLE PRECISION array, dimension (M)
113 *> \endverbatim
114 *>
115 *> \param[out] RESID
116 *> \verbatim
117 *> RESID is DOUBLE PRECISION
118 *> The maximum over the number of right hand sides of
119 *> norm(B - op(A)*X) / ( norm(op(A)) * norm(X) * EPS ).
120 *> \endverbatim
121 *
122 * Authors:
123 * ========
124 *
125 *> \author Univ. of Tennessee
126 *> \author Univ. of California Berkeley
127 *> \author Univ. of Colorado Denver
128 *> \author NAG Ltd.
129 *
130 *> \ingroup double_eig
131 *
132 * =====================================================================
133  SUBROUTINE dget02( TRANS, M, N, NRHS, A, LDA, X, LDX, B, LDB,
134  $ RWORK, RESID )
135 *
136 * -- LAPACK test routine --
137 * -- LAPACK is a software package provided by Univ. of Tennessee, --
138 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
139 *
140 * .. Scalar Arguments ..
141  CHARACTER TRANS
142  INTEGER LDA, LDB, LDX, M, N, NRHS
143  DOUBLE PRECISION RESID
144 * ..
145 * .. Array Arguments ..
146  DOUBLE PRECISION A( LDA, * ), B( LDB, * ), RWORK( * ),
147  $ x( ldx, * )
148 * ..
149 *
150 * =====================================================================
151 *
152 * .. Parameters ..
153  DOUBLE PRECISION ZERO, ONE
154  parameter( zero = 0.0d+0, one = 1.0d+0 )
155 * ..
156 * .. Local Scalars ..
157  INTEGER J, N1, N2
158  DOUBLE PRECISION ANORM, BNORM, EPS, XNORM
159 * ..
160 * .. External Functions ..
161  LOGICAL LSAME
162  DOUBLE PRECISION DASUM, DLAMCH, DLANGE
163  EXTERNAL lsame, dasum, dlamch, dlange
164 * ..
165 * .. External Subroutines ..
166  EXTERNAL dgemm
167 * ..
168 * .. Intrinsic Functions ..
169  INTRINSIC max
170 * ..
171 * .. Executable Statements ..
172 *
173 * Quick exit if M = 0 or N = 0 or NRHS = 0
174 *
175  IF( m.LE.0 .OR. n.LE.0 .OR. nrhs.EQ.0 ) THEN
176  resid = zero
177  RETURN
178  END IF
179 *
180  IF( lsame( trans, 'T' ) .OR. lsame( trans, 'C' ) ) THEN
181  n1 = n
182  n2 = m
183  ELSE
184  n1 = m
185  n2 = n
186  END IF
187 *
188 * Exit with RESID = 1/EPS if ANORM = 0.
189 *
190  eps = dlamch( 'Epsilon' )
191  IF( lsame( trans, 'N' ) ) THEN
192  anorm = dlange( '1', m, n, a, lda, rwork )
193  ELSE
194  anorm = dlange( 'I', m, n, a, lda, rwork )
195  END IF
196  IF( anorm.LE.zero ) THEN
197  resid = one / eps
198  RETURN
199  END IF
200 *
201 * Compute B - op(A)*X and store in B.
202 *
203  CALL dgemm( trans, 'No transpose', n1, nrhs, n2, -one, a, lda, x,
204  $ ldx, one, b, ldb )
205 *
206 * Compute the maximum over the number of right hand sides of
207 * norm(B - op(A)*X) / ( norm(op(A)) * norm(X) * EPS ) .
208 *
209  resid = zero
210  DO 10 j = 1, nrhs
211  bnorm = dasum( n1, b( 1, j ), 1 )
212  xnorm = dasum( n2, x( 1, j ), 1 )
213  IF( xnorm.LE.zero ) THEN
214  resid = one / eps
215  ELSE
216  resid = max( resid, ( ( bnorm / anorm ) / xnorm ) / eps )
217  END IF
218  10 CONTINUE
219 *
220  RETURN
221 *
222 * End of DGET02
223 *
224  END
subroutine dgemm(TRANSA, TRANSB, M, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
DGEMM
Definition: dgemm.f:187
subroutine dget02(TRANS, M, N, NRHS, A, LDA, X, LDX, B, LDB, RWORK, RESID)
DGET02
Definition: dget02.f:135