LAPACK  3.8.0
LAPACK: Linear Algebra PACKage
ctrt02.f
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1 *> \brief \b CTRT02
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 CTRT02( UPLO, TRANS, DIAG, N, NRHS, A, LDA, X, LDX, B,
12 * LDB, WORK, RWORK, RESID )
13 *
14 * .. Scalar Arguments ..
15 * CHARACTER DIAG, TRANS, UPLO
16 * INTEGER LDA, LDB, LDX, N, NRHS
17 * REAL RESID
18 * ..
19 * .. Array Arguments ..
20 * REAL RWORK( * )
21 * COMPLEX A( LDA, * ), B( LDB, * ), WORK( * ),
22 * $ X( LDX, * )
23 * ..
24 *
25 *
26 *> \par Purpose:
27 * =============
28 *>
29 *> \verbatim
30 *>
31 *> CTRT02 computes the residual for the computed solution to a
32 *> triangular system of linear equations A*x = b, A**T *x = b,
33 *> or A**H *x = b. Here A is a triangular matrix, A**T is the transpose
34 *> of A, A**H is the conjugate transpose of A, and x and b are N by NRHS
35 *> matrices. The test ratio is the maximum over the number of right
36 *> hand sides of
37 *> norm(b - op(A)*x) / ( norm(op(A)) * norm(x) * EPS ),
38 *> where op(A) denotes A, A**T, or A**H, and EPS is the machine epsilon.
39 *> \endverbatim
40 *
41 * Arguments:
42 * ==========
43 *
44 *> \param[in] UPLO
45 *> \verbatim
46 *> UPLO is CHARACTER*1
47 *> Specifies whether the matrix A is upper or lower triangular.
48 *> = 'U': Upper triangular
49 *> = 'L': Lower triangular
50 *> \endverbatim
51 *>
52 *> \param[in] TRANS
53 *> \verbatim
54 *> TRANS is CHARACTER*1
55 *> Specifies the operation applied to A.
56 *> = 'N': A *x = b (No transpose)
57 *> = 'T': A**T *x = b (Transpose)
58 *> = 'C': A**H *x = b (Conjugate transpose)
59 *> \endverbatim
60 *>
61 *> \param[in] DIAG
62 *> \verbatim
63 *> DIAG is CHARACTER*1
64 *> Specifies whether or not the matrix A is unit triangular.
65 *> = 'N': Non-unit triangular
66 *> = 'U': Unit triangular
67 *> \endverbatim
68 *>
69 *> \param[in] N
70 *> \verbatim
71 *> N is INTEGER
72 *> The order of the matrix A. N >= 0.
73 *> \endverbatim
74 *>
75 *> \param[in] NRHS
76 *> \verbatim
77 *> NRHS is INTEGER
78 *> The number of right hand sides, i.e., the number of columns
79 *> of the matrices X and B. NRHS >= 0.
80 *> \endverbatim
81 *>
82 *> \param[in] A
83 *> \verbatim
84 *> A is COMPLEX array, dimension (LDA,N)
85 *> The triangular matrix A. If UPLO = 'U', the leading n by n
86 *> upper triangular part of the array A contains the upper
87 *> triangular matrix, and the strictly lower triangular part of
88 *> A is not referenced. If UPLO = 'L', the leading n by n lower
89 *> triangular part of the array A contains the lower triangular
90 *> matrix, and the strictly upper triangular part of A is not
91 *> referenced. If DIAG = 'U', the diagonal elements of A are
92 *> also not referenced and are assumed to be 1.
93 *> \endverbatim
94 *>
95 *> \param[in] LDA
96 *> \verbatim
97 *> LDA is INTEGER
98 *> The leading dimension of the array A. LDA >= max(1,N).
99 *> \endverbatim
100 *>
101 *> \param[in] X
102 *> \verbatim
103 *> X is COMPLEX array, dimension (LDX,NRHS)
104 *> The computed solution vectors for the system of linear
105 *> equations.
106 *> \endverbatim
107 *>
108 *> \param[in] LDX
109 *> \verbatim
110 *> LDX is INTEGER
111 *> The leading dimension of the array X. LDX >= max(1,N).
112 *> \endverbatim
113 *>
114 *> \param[in] B
115 *> \verbatim
116 *> B is COMPLEX array, dimension (LDB,NRHS)
117 *> The right hand side vectors for the system of linear
118 *> equations.
119 *> \endverbatim
120 *>
121 *> \param[in] LDB
122 *> \verbatim
123 *> LDB is INTEGER
124 *> The leading dimension of the array B. LDB >= max(1,N).
125 *> \endverbatim
126 *>
127 *> \param[out] WORK
128 *> \verbatim
129 *> WORK is COMPLEX array, dimension (N)
130 *> \endverbatim
131 *>
132 *> \param[out] RWORK
133 *> \verbatim
134 *> RWORK is REAL array, dimension (N)
135 *> \endverbatim
136 *>
137 *> \param[out] RESID
138 *> \verbatim
139 *> RESID is REAL
140 *> The maximum over the number of right hand sides of
141 *> norm(op(A)*x - b) / ( norm(op(A)) * norm(x) * EPS ).
142 *> \endverbatim
143 *
144 * Authors:
145 * ========
146 *
147 *> \author Univ. of Tennessee
148 *> \author Univ. of California Berkeley
149 *> \author Univ. of Colorado Denver
150 *> \author NAG Ltd.
151 *
152 *> \date December 2016
153 *
154 *> \ingroup complex_lin
155 *
156 * =====================================================================
157  SUBROUTINE ctrt02( UPLO, TRANS, DIAG, N, NRHS, A, LDA, X, LDX, B,
158  $ LDB, WORK, RWORK, RESID )
159 *
160 * -- LAPACK test routine (version 3.7.0) --
161 * -- LAPACK is a software package provided by Univ. of Tennessee, --
162 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
163 * December 2016
164 *
165 * .. Scalar Arguments ..
166  CHARACTER DIAG, TRANS, UPLO
167  INTEGER LDA, LDB, LDX, N, NRHS
168  REAL RESID
169 * ..
170 * .. Array Arguments ..
171  REAL RWORK( * )
172  COMPLEX A( lda, * ), B( ldb, * ), WORK( * ),
173  $ x( ldx, * )
174 * ..
175 *
176 * =====================================================================
177 *
178 * .. Parameters ..
179  REAL ZERO, ONE
180  parameter( zero = 0.0e+0, one = 1.0e+0 )
181 * ..
182 * .. Local Scalars ..
183  INTEGER J
184  REAL ANORM, BNORM, EPS, XNORM
185 * ..
186 * .. External Functions ..
187  LOGICAL LSAME
188  REAL CLANTR, SCASUM, SLAMCH
189  EXTERNAL lsame, clantr, scasum, slamch
190 * ..
191 * .. External Subroutines ..
192  EXTERNAL caxpy, ccopy, ctrmv
193 * ..
194 * .. Intrinsic Functions ..
195  INTRINSIC cmplx, max
196 * ..
197 * .. Executable Statements ..
198 *
199 * Quick exit if N = 0 or NRHS = 0
200 *
201  IF( n.LE.0 .OR. nrhs.LE.0 ) THEN
202  resid = zero
203  RETURN
204  END IF
205 *
206 * Compute the 1-norm of A or A**H.
207 *
208  IF( lsame( trans, 'N' ) ) THEN
209  anorm = clantr( '1', uplo, diag, n, n, a, lda, rwork )
210  ELSE
211  anorm = clantr( 'I', uplo, diag, n, n, a, lda, rwork )
212  END IF
213 *
214 * Exit with RESID = 1/EPS if ANORM = 0.
215 *
216  eps = slamch( 'Epsilon' )
217  IF( anorm.LE.zero ) THEN
218  resid = one / eps
219  RETURN
220  END IF
221 *
222 * Compute the maximum over the number of right hand sides of
223 * norm(op(A)*x - b) / ( norm(op(A)) * norm(x) * EPS )
224 *
225  resid = zero
226  DO 10 j = 1, nrhs
227  CALL ccopy( n, x( 1, j ), 1, work, 1 )
228  CALL ctrmv( uplo, trans, diag, n, a, lda, work, 1 )
229  CALL caxpy( n, cmplx( -one ), b( 1, j ), 1, work, 1 )
230  bnorm = scasum( n, work, 1 )
231  xnorm = scasum( n, x( 1, j ), 1 )
232  IF( xnorm.LE.zero ) THEN
233  resid = one / eps
234  ELSE
235  resid = max( resid, ( ( bnorm / anorm ) / xnorm ) / eps )
236  END IF
237  10 CONTINUE
238 *
239  RETURN
240 *
241 * End of CTRT02
242 *
243  END
subroutine caxpy(N, CA, CX, INCX, CY, INCY)
CAXPY
Definition: caxpy.f:90
subroutine ccopy(N, CX, INCX, CY, INCY)
CCOPY
Definition: ccopy.f:83
subroutine ctrmv(UPLO, TRANS, DIAG, N, A, LDA, X, INCX)
CTRMV
Definition: ctrmv.f:149
subroutine ctrt02(UPLO, TRANS, DIAG, N, NRHS, A, LDA, X, LDX, B, LDB, WORK, RWORK, RESID)
CTRT02
Definition: ctrt02.f:159