LAPACK  3.8.0
LAPACK: Linear Algebra PACKage
strt02.f
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1 *> \brief \b STRT02
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 STRT02( UPLO, TRANS, DIAG, N, NRHS, A, LDA, X, LDX, B,
12 * LDB, WORK, 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 A( LDA, * ), B( LDB, * ), WORK( * ),
21 * $ X( LDX, * )
22 * ..
23 *
24 *
25 *> \par Purpose:
26 * =============
27 *>
28 *> \verbatim
29 *>
30 *> STRT02 computes the residual for the computed solution to a
31 *> triangular system of linear equations A*x = b or A'*x = b.
32 *> Here A is a triangular matrix, A' is the transpose of A, and x and b
33 *> are N by NRHS matrices. The test ratio is the maximum over the
34 *> number of right hand sides of
35 *> norm(b - op(A)*x) / ( norm(op(A)) * norm(x) * EPS ),
36 *> where op(A) denotes A or A' and EPS is the machine epsilon.
37 *> \endverbatim
38 *
39 * Arguments:
40 * ==========
41 *
42 *> \param[in] UPLO
43 *> \verbatim
44 *> UPLO is CHARACTER*1
45 *> Specifies whether the matrix A is upper or lower triangular.
46 *> = 'U': Upper triangular
47 *> = 'L': Lower triangular
48 *> \endverbatim
49 *>
50 *> \param[in] TRANS
51 *> \verbatim
52 *> TRANS is CHARACTER*1
53 *> Specifies the operation applied to A.
54 *> = 'N': A *x = b (No transpose)
55 *> = 'T': A'*x = b (Transpose)
56 *> = 'C': A'*x = b (Conjugate transpose = Transpose)
57 *> \endverbatim
58 *>
59 *> \param[in] DIAG
60 *> \verbatim
61 *> DIAG is CHARACTER*1
62 *> Specifies whether or not the matrix A is unit triangular.
63 *> = 'N': Non-unit triangular
64 *> = 'U': Unit triangular
65 *> \endverbatim
66 *>
67 *> \param[in] N
68 *> \verbatim
69 *> N is INTEGER
70 *> The order of the matrix A. N >= 0.
71 *> \endverbatim
72 *>
73 *> \param[in] NRHS
74 *> \verbatim
75 *> NRHS is INTEGER
76 *> The number of right hand sides, i.e., the number of columns
77 *> of the matrices X and B. NRHS >= 0.
78 *> \endverbatim
79 *>
80 *> \param[in] A
81 *> \verbatim
82 *> A is REAL array, dimension (LDA,N)
83 *> The triangular matrix A. If UPLO = 'U', the leading n by n
84 *> upper triangular part of the array A contains the upper
85 *> triangular matrix, and the strictly lower triangular part of
86 *> A is not referenced. If UPLO = 'L', the leading n by n lower
87 *> triangular part of the array A contains the lower triangular
88 *> matrix, and the strictly upper triangular part of A is not
89 *> referenced. If DIAG = 'U', the diagonal elements of A are
90 *> also not referenced and are assumed to be 1.
91 *> \endverbatim
92 *>
93 *> \param[in] LDA
94 *> \verbatim
95 *> LDA is INTEGER
96 *> The leading dimension of the array A. LDA >= max(1,N).
97 *> \endverbatim
98 *>
99 *> \param[in] X
100 *> \verbatim
101 *> X is REAL array, dimension (LDX,NRHS)
102 *> The computed solution vectors for the system of linear
103 *> equations.
104 *> \endverbatim
105 *>
106 *> \param[in] LDX
107 *> \verbatim
108 *> LDX is INTEGER
109 *> The leading dimension of the array X. LDX >= max(1,N).
110 *> \endverbatim
111 *>
112 *> \param[in] B
113 *> \verbatim
114 *> B is REAL array, dimension (LDB,NRHS)
115 *> The right hand side vectors for the system of linear
116 *> equations.
117 *> \endverbatim
118 *>
119 *> \param[in] LDB
120 *> \verbatim
121 *> LDB is INTEGER
122 *> The leading dimension of the array B. LDB >= max(1,N).
123 *> \endverbatim
124 *>
125 *> \param[out] WORK
126 *> \verbatim
127 *> WORK is REAL array, dimension (N)
128 *> \endverbatim
129 *>
130 *> \param[out] RESID
131 *> \verbatim
132 *> RESID is REAL
133 *> The maximum over the number of right hand sides of
134 *> norm(op(A)*x - b) / ( norm(op(A)) * norm(x) * EPS ).
135 *> \endverbatim
136 *
137 * Authors:
138 * ========
139 *
140 *> \author Univ. of Tennessee
141 *> \author Univ. of California Berkeley
142 *> \author Univ. of Colorado Denver
143 *> \author NAG Ltd.
144 *
145 *> \date December 2016
146 *
147 *> \ingroup single_lin
148 *
149 * =====================================================================
150  SUBROUTINE strt02( UPLO, TRANS, DIAG, N, NRHS, A, LDA, X, LDX, B,
151  $ LDB, WORK, RESID )
152 *
153 * -- LAPACK test routine (version 3.7.0) --
154 * -- LAPACK is a software package provided by Univ. of Tennessee, --
155 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
156 * December 2016
157 *
158 * .. Scalar Arguments ..
159  CHARACTER DIAG, TRANS, UPLO
160  INTEGER LDA, LDB, LDX, N, NRHS
161  REAL RESID
162 * ..
163 * .. Array Arguments ..
164  REAL A( lda, * ), B( ldb, * ), WORK( * ),
165  $ x( ldx, * )
166 * ..
167 *
168 * =====================================================================
169 *
170 * .. Parameters ..
171  REAL ZERO, ONE
172  parameter( zero = 0.0e+0, one = 1.0e+0 )
173 * ..
174 * .. Local Scalars ..
175  INTEGER J
176  REAL ANORM, BNORM, EPS, XNORM
177 * ..
178 * .. External Functions ..
179  LOGICAL LSAME
180  REAL SASUM, SLAMCH, SLANTR
181  EXTERNAL lsame, sasum, slamch, slantr
182 * ..
183 * .. External Subroutines ..
184  EXTERNAL saxpy, scopy, strmv
185 * ..
186 * .. Intrinsic Functions ..
187  INTRINSIC max
188 * ..
189 * .. Executable Statements ..
190 *
191 * Quick exit if N = 0 or NRHS = 0
192 *
193  IF( n.LE.0 .OR. nrhs.LE.0 ) THEN
194  resid = zero
195  RETURN
196  END IF
197 *
198 * Compute the 1-norm of A or A'.
199 *
200  IF( lsame( trans, 'N' ) ) THEN
201  anorm = slantr( '1', uplo, diag, n, n, a, lda, work )
202  ELSE
203  anorm = slantr( 'I', uplo, diag, n, n, a, lda, work )
204  END IF
205 *
206 * Exit with RESID = 1/EPS if ANORM = 0.
207 *
208  eps = slamch( 'Epsilon' )
209  IF( anorm.LE.zero ) THEN
210  resid = one / eps
211  RETURN
212  END IF
213 *
214 * Compute the maximum over the number of right hand sides of
215 * norm(op(A)*x - b) / ( norm(op(A)) * norm(x) * EPS )
216 *
217  resid = zero
218  DO 10 j = 1, nrhs
219  CALL scopy( n, x( 1, j ), 1, work, 1 )
220  CALL strmv( uplo, trans, diag, n, a, lda, work, 1 )
221  CALL saxpy( n, -one, b( 1, j ), 1, work, 1 )
222  bnorm = sasum( n, work, 1 )
223  xnorm = sasum( n, x( 1, j ), 1 )
224  IF( xnorm.LE.zero ) THEN
225  resid = one / eps
226  ELSE
227  resid = max( resid, ( ( bnorm / anorm ) / xnorm ) / eps )
228  END IF
229  10 CONTINUE
230 *
231  RETURN
232 *
233 * End of STRT02
234 *
235  END
subroutine strmv(UPLO, TRANS, DIAG, N, A, LDA, X, INCX)
STRMV
Definition: strmv.f:149
subroutine saxpy(N, SA, SX, INCX, SY, INCY)
SAXPY
Definition: saxpy.f:91
subroutine strt02(UPLO, TRANS, DIAG, N, NRHS, A, LDA, X, LDX, B, LDB, WORK, RESID)
STRT02
Definition: strt02.f:152
subroutine scopy(N, SX, INCX, SY, INCY)
SCOPY
Definition: scopy.f:84