LAPACK  3.8.0
LAPACK: Linear Algebra PACKage
zget08.f
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1 *> \brief \b ZGET08
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 ZGET08( 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 RWORK( * )
21 * COMPLEX*16 A( LDA, * ), B( LDB, * ), X( LDX, * )
22 * ..
23 *
24 *
25 *> \par Purpose:
26 * =============
27 *>
28 *> \verbatim
29 *>
30 *> ZGET08 computes the residual for a solution of a system of linear
31 *> equations A*x = b or A'*x = b:
32 *> RESID = norm(B - A*X) / ( norm(A) * norm(X) * EPS ),
33 *> where EPS is the machine epsilon.
34 *> \endverbatim
35 *
36 * Arguments:
37 * ==========
38 *
39 *> \param[in] TRANS
40 *> \verbatim
41 *> TRANS is CHARACTER*1
42 *> Specifies the form of the system of equations:
43 *> = 'N': A *x = b
44 *> = 'T': A^T*x = b, where A^T is the transpose of A
45 *> = 'C': A^H*x = b, where A^H is the conjugate transpose of A
46 *> \endverbatim
47 *>
48 *> \param[in] M
49 *> \verbatim
50 *> M is INTEGER
51 *> The number of rows of the matrix A. M >= 0.
52 *> \endverbatim
53 *>
54 *> \param[in] N
55 *> \verbatim
56 *> N is INTEGER
57 *> The number of columns of the matrix A. N >= 0.
58 *> \endverbatim
59 *>
60 *> \param[in] NRHS
61 *> \verbatim
62 *> NRHS is INTEGER
63 *> The number of columns of B, the matrix of right hand sides.
64 *> NRHS >= 0.
65 *> \endverbatim
66 *>
67 *> \param[in] A
68 *> \verbatim
69 *> A is COMPLEX*16 array, dimension (LDA,N)
70 *> The original M x N matrix A.
71 *> \endverbatim
72 *>
73 *> \param[in] LDA
74 *> \verbatim
75 *> LDA is INTEGER
76 *> The leading dimension of the array A. LDA >= max(1,M).
77 *> \endverbatim
78 *>
79 *> \param[in] X
80 *> \verbatim
81 *> X is COMPLEX*16 array, dimension (LDX,NRHS)
82 *> The computed solution vectors for the system of linear
83 *> equations.
84 *> \endverbatim
85 *>
86 *> \param[in] LDX
87 *> \verbatim
88 *> LDX is INTEGER
89 *> The leading dimension of the array X. If TRANS = 'N',
90 *> LDX >= max(1,N); if TRANS = 'T' or 'C', LDX >= max(1,M).
91 *> \endverbatim
92 *>
93 *> \param[in,out] B
94 *> \verbatim
95 *> B is COMPLEX*16 array, dimension (LDB,NRHS)
96 *> On entry, the right hand side vectors for the system of
97 *> linear equations.
98 *> On exit, B is overwritten with the difference B - A*X.
99 *> \endverbatim
100 *>
101 *> \param[in] LDB
102 *> \verbatim
103 *> LDB is INTEGER
104 *> The leading dimension of the array B. IF TRANS = 'N',
105 *> LDB >= max(1,M); if TRANS = 'T' or 'C', LDB >= max(1,N).
106 *> \endverbatim
107 *>
108 *> \param[out] RWORK
109 *> \verbatim
110 *> RWORK is DOUBLE PRECISION array, dimension (M)
111 *> \endverbatim
112 *>
113 *> \param[out] RESID
114 *> \verbatim
115 *> RESID is DOUBLE PRECISION
116 *> The maximum over the number of right hand sides of
117 *> norm(B - A*X) / ( norm(A) * norm(X) * EPS ).
118 *> \endverbatim
119 *
120 * Authors:
121 * ========
122 *
123 *> \author Univ. of Tennessee
124 *> \author Univ. of California Berkeley
125 *> \author Univ. of Colorado Denver
126 *> \author NAG Ltd.
127 *
128 *> \date December 2016
129 *
130 *> \ingroup complex16_lin
131 *
132 * =====================================================================
133  SUBROUTINE zget08( TRANS, M, N, NRHS, A, LDA, X, LDX, B, LDB,
134  $ RWORK, RESID )
135 *
136 * -- LAPACK test routine (version 3.7.0) --
137 * -- LAPACK is a software package provided by Univ. of Tennessee, --
138 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
139 * December 2016
140 *
141 * .. Scalar Arguments ..
142  CHARACTER TRANS
143  INTEGER LDA, LDB, LDX, M, N, NRHS
144  DOUBLE PRECISION RESID
145 * ..
146 * .. Array Arguments ..
147  DOUBLE PRECISION RWORK( * )
148  COMPLEX*16 A( lda, * ), B( ldb, * ), X( ldx, * )
149 * ..
150 *
151 * =====================================================================
152 *
153 * .. Parameters ..
154  DOUBLE PRECISION ZERO, ONE
155  parameter( zero = 0.0d+0, one = 1.0d+0 )
156  COMPLEX*16 CONE
157  parameter( cone = ( 1.0d+0, 0.0d+0 ) )
158 * ..
159 * .. Local Scalars ..
160  INTEGER J, N1, N2
161  DOUBLE PRECISION ANORM, BNORM, EPS, XNORM
162  COMPLEX*16 ZDUM
163 * ..
164 * .. External Functions ..
165  LOGICAL LSAME
166  INTEGER IZAMAX
167  DOUBLE PRECISION DLAMCH, ZLANGE
168  EXTERNAL lsame, izamax, dlamch, zlange
169 * ..
170 * .. External Subroutines ..
171  EXTERNAL zgemm
172 * ..
173 * .. Intrinsic Functions ..
174  INTRINSIC abs, dble, dimag, max
175 * ..
176 * .. Statement Functions ..
177  DOUBLE PRECISION CABS1
178 * ..
179 * .. Statement Function definitions ..
180  cabs1( zdum ) = abs( dble( zdum ) ) + abs( dimag( zdum ) )
181 * ..
182 * .. Executable Statements ..
183 *
184 * Quick exit if M = 0 or N = 0 or NRHS = 0
185 *
186  IF( m.LE.0 .OR. n.LE.0 .OR. nrhs.EQ.0 ) THEN
187  resid = zero
188  RETURN
189  END IF
190 *
191  IF( lsame( trans, 'T' ) .OR. lsame( trans, 'C' ) ) THEN
192  n1 = n
193  n2 = m
194  ELSE
195  n1 = m
196  n2 = n
197  END IF
198 *
199 * Exit with RESID = 1/EPS if ANORM = 0.
200 *
201  eps = dlamch( 'Epsilon' )
202  anorm = zlange( 'I', n1, n2, a, lda, rwork )
203  IF( anorm.LE.zero ) THEN
204  resid = one / eps
205  RETURN
206  END IF
207 *
208 * Compute B - A*X (or B - A'*X ) and store in B.
209 *
210  CALL zgemm( trans, 'No transpose', n1, nrhs, n2, -cone, a, lda, x,
211  $ ldx, cone, b, ldb )
212 *
213 * Compute the maximum over the number of right hand sides of
214 * norm(B - A*X) / ( norm(A) * norm(X) * EPS ) .
215 *
216  resid = zero
217  DO 10 j = 1, nrhs
218  bnorm = cabs1( b( izamax( n1, b( 1, j ), 1 ), j ) )
219  xnorm = cabs1( x( izamax( n2, x( 1, j ), 1 ), j ) )
220  IF( xnorm.LE.zero ) THEN
221  resid = one / eps
222  ELSE
223  resid = max( resid, ( ( bnorm / anorm ) / xnorm ) / eps )
224  END IF
225  10 CONTINUE
226 *
227  RETURN
228 *
229 * End of ZGET02
230 *
231  END
subroutine zgemm(TRANSA, TRANSB, M, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
ZGEMM
Definition: zgemm.f:189
subroutine zget08(TRANS, M, N, NRHS, A, LDA, X, LDX, B, LDB, RWORK, RESID)
ZGET08
Definition: zget08.f:135