LAPACK  3.10.1 LAPACK: Linear Algebra PACKage
zget02.f
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1 *> \brief \b ZGET02
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 ZGET02( 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 *> ZGET02 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, A**T, or A**H, depending on TRANS, and EPS is the
34 *> machine epsilon.
35 *> \endverbatim
36 *
37 * Arguments:
38 * ==========
39 *
40 *> \param[in] TRANS
41 *> \verbatim
42 *> TRANS is CHARACTER*1
43 *> Specifies the form of the system of equations:
44 *> = 'N': A * X = B (No transpose)
45 *> = 'T': A**T * X = B (Transpose)
46 *> = 'C': A**H * X = B (Conjugate transpose)
47 *> \endverbatim
48 *>
49 *> \param[in] M
50 *> \verbatim
51 *> M is INTEGER
52 *> The number of rows of the matrix A. M >= 0.
53 *> \endverbatim
54 *>
55 *> \param[in] N
56 *> \verbatim
57 *> N is INTEGER
58 *> The number of columns of the matrix A. N >= 0.
59 *> \endverbatim
60 *>
61 *> \param[in] NRHS
62 *> \verbatim
63 *> NRHS is INTEGER
64 *> The number of columns of B, the matrix of right hand sides.
65 *> NRHS >= 0.
66 *> \endverbatim
67 *>
68 *> \param[in] A
69 *> \verbatim
70 *> A is COMPLEX*16 array, dimension (LDA,N)
71 *> The original M x N matrix A.
72 *> \endverbatim
73 *>
74 *> \param[in] LDA
75 *> \verbatim
76 *> LDA is INTEGER
77 *> The leading dimension of the array A. LDA >= max(1,M).
78 *> \endverbatim
79 *>
80 *> \param[in] X
81 *> \verbatim
82 *> X is COMPLEX*16 array, dimension (LDX,NRHS)
83 *> The computed solution vectors for the system of linear
84 *> equations.
85 *> \endverbatim
86 *>
87 *> \param[in] LDX
88 *> \verbatim
89 *> LDX is INTEGER
90 *> The leading dimension of the array X. If TRANS = 'N',
91 *> LDX >= max(1,N); if TRANS = 'T' or 'C', LDX >= max(1,M).
92 *> \endverbatim
93 *>
94 *> \param[in,out] B
95 *> \verbatim
96 *> B is COMPLEX*16 array, dimension (LDB,NRHS)
97 *> On entry, the right hand side vectors for the system of
98 *> linear equations.
99 *> On exit, B is overwritten with the difference B - A*X.
100 *> \endverbatim
101 *>
102 *> \param[in] LDB
103 *> \verbatim
104 *> LDB is INTEGER
105 *> The leading dimension of the array B. IF TRANS = 'N',
106 *> LDB >= max(1,M); if TRANS = 'T' or 'C', LDB >= max(1,N).
107 *> \endverbatim
108 *>
109 *> \param[out] RWORK
110 *> \verbatim
111 *> RWORK is DOUBLE PRECISION array, dimension (M)
112 *> \endverbatim
113 *>
114 *> \param[out] RESID
115 *> \verbatim
116 *> RESID is DOUBLE PRECISION
117 *> The maximum over the number of right hand sides of
118 *> norm(B - op(A)*X) / ( norm(op(A)) * norm(X) * EPS ).
119 *> \endverbatim
120 *
121 * Authors:
122 * ========
123 *
124 *> \author Univ. of Tennessee
125 *> \author Univ. of California Berkeley
126 *> \author Univ. of Colorado Denver
127 *> \author NAG Ltd.
128 *
129 *> \ingroup complex16_eig
130 *
131 * =====================================================================
132  SUBROUTINE zget02( TRANS, M, N, NRHS, A, LDA, X, LDX, B, LDB,
133  \$ RWORK, RESID )
134 *
135 * -- LAPACK test routine --
136 * -- LAPACK is a software package provided by Univ. of Tennessee, --
137 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
138 *
139 * .. Scalar Arguments ..
140  CHARACTER TRANS
141  INTEGER LDA, LDB, LDX, M, N, NRHS
142  DOUBLE PRECISION RESID
143 * ..
144 * .. Array Arguments ..
145  DOUBLE PRECISION RWORK( * )
146  COMPLEX*16 A( LDA, * ), B( LDB, * ), X( LDX, * )
147 * ..
148 *
149 * =====================================================================
150 *
151 * .. Parameters ..
152  DOUBLE PRECISION ZERO, ONE
153  parameter( zero = 0.0d+0, one = 1.0d+0 )
154  COMPLEX*16 CONE
155  parameter( cone = ( 1.0d+0, 0.0d+0 ) )
156 * ..
157 * .. Local Scalars ..
158  INTEGER J, N1, N2
159  DOUBLE PRECISION ANORM, BNORM, EPS, XNORM
160 * ..
161 * .. External Functions ..
162  LOGICAL LSAME
163  DOUBLE PRECISION DLAMCH, DZASUM, ZLANGE
164  EXTERNAL lsame, dlamch, dzasum, zlange
165 * ..
166 * .. External Subroutines ..
167  EXTERNAL zgemm
168 * ..
169 * .. Intrinsic Functions ..
170  INTRINSIC max
171 * ..
172 * .. Executable Statements ..
173 *
174 * Quick exit if M = 0 or N = 0 or NRHS = 0
175 *
176  IF( m.LE.0 .OR. n.LE.0 .OR. nrhs.EQ.0 ) THEN
177  resid = zero
178  RETURN
179  END IF
180 *
181  IF( lsame( trans, 'T' ) .OR. lsame( trans, 'C' ) ) THEN
182  n1 = n
183  n2 = m
184  ELSE
185  n1 = m
186  n2 = n
187  END IF
188 *
189 * Exit with RESID = 1/EPS if ANORM = 0.
190 *
191  eps = dlamch( 'Epsilon' )
192  IF( lsame( trans, 'N' ) ) THEN
193  anorm = zlange( '1', m, n, a, lda, rwork )
194  ELSE
195  anorm = zlange( 'I', m, n, a, lda, rwork )
196  END IF
197  IF( anorm.LE.zero ) THEN
198  resid = one / eps
199  RETURN
200  END IF
201 *
202 * Compute B - op(A)*X and store in B.
203 *
204  CALL zgemm( trans, 'No transpose', n1, nrhs, n2, -cone, a, lda, x,
205  \$ ldx, cone, b, ldb )
206 *
207 * Compute the maximum over the number of right hand sides of
208 * norm(B - op(A)*X) / ( norm(op(A)) * norm(X) * EPS ) .
209 *
210  resid = zero
211  DO 10 j = 1, nrhs
212  bnorm = dzasum( n1, b( 1, j ), 1 )
213  xnorm = dzasum( n2, x( 1, j ), 1 )
214  IF( xnorm.LE.zero ) THEN
215  resid = one / eps
216  ELSE
217  resid = max( resid, ( ( bnorm / anorm ) / xnorm ) / eps )
218  END IF
219  10 CONTINUE
220 *
221  RETURN
222 *
223 * End of ZGET02
224 *
225  END
subroutine zgemm(TRANSA, TRANSB, M, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
ZGEMM
Definition: zgemm.f:187
subroutine zget02(TRANS, M, N, NRHS, A, LDA, X, LDX, B, LDB, RWORK, RESID)
ZGET02
Definition: zget02.f:134