LAPACK  3.10.0 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 *> The norm used is the 1-norm.
38 *> \endverbatim
39 *
40 * Arguments:
41 * ==========
42 *
43 *> \param[in] UPLO
44 *> \verbatim
45 *> UPLO is CHARACTER*1
46 *> Specifies whether the matrix A is upper or lower triangular.
47 *> = 'U': Upper triangular
48 *> = 'L': Lower triangular
49 *> \endverbatim
50 *>
51 *> \param[in] TRANS
52 *> \verbatim
53 *> TRANS is CHARACTER*1
54 *> Specifies the operation applied to A.
55 *> = 'N': A *x = b (No transpose)
56 *> = 'T': A'*x = b (Transpose)
57 *> = 'C': A'*x = b (Conjugate transpose = Transpose)
58 *> \endverbatim
59 *>
60 *> \param[in] DIAG
61 *> \verbatim
62 *> DIAG is CHARACTER*1
63 *> Specifies whether or not the matrix A is unit triangular.
64 *> = 'N': Non-unit triangular
65 *> = 'U': Unit triangular
66 *> \endverbatim
67 *>
68 *> \param[in] N
69 *> \verbatim
70 *> N is INTEGER
71 *> The order of the matrix A. N >= 0.
72 *> \endverbatim
73 *>
74 *> \param[in] NRHS
75 *> \verbatim
76 *> NRHS is INTEGER
77 *> The number of right hand sides, i.e., the number of columns
78 *> of the matrices X and B. NRHS >= 0.
79 *> \endverbatim
80 *>
81 *> \param[in] A
82 *> \verbatim
83 *> A is REAL array, dimension (LDA,N)
84 *> The triangular matrix A. If UPLO = 'U', the leading n by n
85 *> upper triangular part of the array A contains the upper
86 *> triangular matrix, and the strictly lower triangular part of
87 *> A is not referenced. If UPLO = 'L', the leading n by n lower
88 *> triangular part of the array A contains the lower triangular
89 *> matrix, and the strictly upper triangular part of A is not
90 *> referenced. If DIAG = 'U', the diagonal elements of A are
91 *> also not referenced and are assumed to be 1.
92 *> \endverbatim
93 *>
94 *> \param[in] LDA
95 *> \verbatim
96 *> LDA is INTEGER
97 *> The leading dimension of the array A. LDA >= max(1,N).
98 *> \endverbatim
99 *>
100 *> \param[in] X
101 *> \verbatim
102 *> X is REAL array, dimension (LDX,NRHS)
103 *> The computed solution vectors for the system of linear
104 *> equations.
105 *> \endverbatim
106 *>
107 *> \param[in] LDX
108 *> \verbatim
109 *> LDX is INTEGER
110 *> The leading dimension of the array X. LDX >= max(1,N).
111 *> \endverbatim
112 *>
113 *> \param[in] B
114 *> \verbatim
115 *> B is REAL array, dimension (LDB,NRHS)
116 *> The right hand side vectors for the system of linear
117 *> equations.
118 *> \endverbatim
119 *>
120 *> \param[in] LDB
121 *> \verbatim
122 *> LDB is INTEGER
123 *> The leading dimension of the array B. LDB >= max(1,N).
124 *> \endverbatim
125 *>
126 *> \param[out] WORK
127 *> \verbatim
128 *> WORK is REAL array, dimension (N)
129 *> \endverbatim
130 *>
131 *> \param[out] RESID
132 *> \verbatim
133 *> RESID is REAL
134 *> The maximum over the number of right hand sides of
135 *> norm(op(A)*x - b) / ( norm(op(A)) * norm(x) * EPS ).
136 *> \endverbatim
137 *
138 * Authors:
139 * ========
140 *
141 *> \author Univ. of Tennessee
142 *> \author Univ. of California Berkeley
143 *> \author Univ. of Colorado Denver
144 *> \author NAG Ltd.
145 *
146 *> \ingroup single_lin
147 *
148 * =====================================================================
149  SUBROUTINE strt02( UPLO, TRANS, DIAG, N, NRHS, A, LDA, X, LDX, B,
150  \$ LDB, WORK, RESID )
151 *
152 * -- LAPACK test routine --
153 * -- LAPACK is a software package provided by Univ. of Tennessee, --
154 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
155 *
156 * .. Scalar Arguments ..
157  CHARACTER DIAG, TRANS, UPLO
158  INTEGER LDA, LDB, LDX, N, NRHS
159  REAL RESID
160 * ..
161 * .. Array Arguments ..
162  REAL A( LDA, * ), B( LDB, * ), WORK( * ),
163  \$ x( ldx, * )
164 * ..
165 *
166 * =====================================================================
167 *
168 * .. Parameters ..
169  REAL ZERO, ONE
170  parameter( zero = 0.0e+0, one = 1.0e+0 )
171 * ..
172 * .. Local Scalars ..
173  INTEGER J
174  REAL ANORM, BNORM, EPS, XNORM
175 * ..
176 * .. External Functions ..
177  LOGICAL LSAME
178  REAL SASUM, SLAMCH, SLANTR
179  EXTERNAL lsame, sasum, slamch, slantr
180 * ..
181 * .. External Subroutines ..
182  EXTERNAL saxpy, scopy, strmv
183 * ..
184 * .. Intrinsic Functions ..
185  INTRINSIC max
186 * ..
187 * .. Executable Statements ..
188 *
189 * Quick exit if N = 0 or NRHS = 0
190 *
191  IF( n.LE.0 .OR. nrhs.LE.0 ) THEN
192  resid = zero
193  RETURN
194  END IF
195 *
196 * Compute the 1-norm of A or A'.
197 *
198  IF( lsame( trans, 'N' ) ) THEN
199  anorm = slantr( '1', uplo, diag, n, n, a, lda, work )
200  ELSE
201  anorm = slantr( 'I', uplo, diag, n, n, a, lda, work )
202  END IF
203 *
204 * Exit with RESID = 1/EPS if ANORM = 0.
205 *
206  eps = slamch( 'Epsilon' )
207  IF( anorm.LE.zero ) THEN
208  resid = one / eps
209  RETURN
210  END IF
211 *
212 * Compute the maximum over the number of right hand sides of
213 * norm(op(A)*x - b) / ( norm(op(A)) * norm(x) * EPS )
214 *
215  resid = zero
216  DO 10 j = 1, nrhs
217  CALL scopy( n, x( 1, j ), 1, work, 1 )
218  CALL strmv( uplo, trans, diag, n, a, lda, work, 1 )
219  CALL saxpy( n, -one, b( 1, j ), 1, work, 1 )
220  bnorm = sasum( n, work, 1 )
221  xnorm = sasum( n, x( 1, j ), 1 )
222  IF( xnorm.LE.zero ) THEN
223  resid = one / eps
224  ELSE
225  resid = max( resid, ( ( bnorm / anorm ) / xnorm ) / eps )
226  END IF
227  10 CONTINUE
228 *
229  RETURN
230 *
231 * End of STRT02
232 *
233  END
subroutine scopy(N, SX, INCX, SY, INCY)
SCOPY
Definition: scopy.f:82
subroutine saxpy(N, SA, SX, INCX, SY, INCY)
SAXPY
Definition: saxpy.f:89
subroutine strmv(UPLO, TRANS, DIAG, N, A, LDA, X, INCX)
STRMV
Definition: strmv.f:147
subroutine strt02(UPLO, TRANS, DIAG, N, NRHS, A, LDA, X, LDX, B, LDB, WORK, RESID)
STRT02
Definition: strt02.f:151