LAPACK  3.10.1
LAPACK: Linear Algebra PACKage
dtrt02.f
Go to the documentation of this file.
1 *> \brief \b DTRT02
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 DTRT02( 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 * DOUBLE PRECISION RESID
18 * ..
19 * .. Array Arguments ..
20 * DOUBLE PRECISION A( LDA, * ), B( LDB, * ), WORK( * ),
21 * $ X( LDX, * )
22 * ..
23 *
24 *
25 *> \par Purpose:
26 * =============
27 *>
28 *> \verbatim
29 *>
30 *> DTRT02 computes the residual for the computed solution to a
31 *> triangular system of linear equations op(A)*X = B, where A is a
32 *> triangular matrix. The test ratio is the maximum over
33 *> norm(b - op(A)*x) / ( ||op(A)||_1 * norm(x) * EPS ),
34 *> where op(A) = A or A**T, b is the column of B, x is the solution
35 *> vector, and EPS is the machine epsilon.
36 *> The norm used is the 1-norm.
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**T * X = B (Transpose)
56 *> = 'C': A**H * 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION array, dimension (N)
128 *> \endverbatim
129 *>
130 *> \param[out] RESID
131 *> \verbatim
132 *> RESID is DOUBLE PRECISION
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 *> \ingroup double_lin
146 *
147 * =====================================================================
148  SUBROUTINE dtrt02( UPLO, TRANS, DIAG, N, NRHS, A, LDA, X, LDX, B,
149  $ LDB, WORK, RESID )
150 *
151 * -- LAPACK test routine --
152 * -- LAPACK is a software package provided by Univ. of Tennessee, --
153 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
154 *
155 * .. Scalar Arguments ..
156  CHARACTER DIAG, TRANS, UPLO
157  INTEGER LDA, LDB, LDX, N, NRHS
158  DOUBLE PRECISION RESID
159 * ..
160 * .. Array Arguments ..
161  DOUBLE PRECISION A( LDA, * ), B( LDB, * ), WORK( * ),
162  $ x( ldx, * )
163 * ..
164 *
165 * =====================================================================
166 *
167 * .. Parameters ..
168  DOUBLE PRECISION ZERO, ONE
169  parameter( zero = 0.0d+0, one = 1.0d+0 )
170 * ..
171 * .. Local Scalars ..
172  INTEGER J
173  DOUBLE PRECISION ANORM, BNORM, EPS, XNORM
174 * ..
175 * .. External Functions ..
176  LOGICAL LSAME
177  DOUBLE PRECISION DASUM, DLAMCH, DLANTR
178  EXTERNAL lsame, dasum, dlamch, dlantr
179 * ..
180 * .. External Subroutines ..
181  EXTERNAL daxpy, dcopy, dtrmv
182 * ..
183 * .. Intrinsic Functions ..
184  INTRINSIC max
185 * ..
186 * .. Executable Statements ..
187 *
188 * Quick exit if N = 0 or NRHS = 0
189 *
190  IF( n.LE.0 .OR. nrhs.LE.0 ) THEN
191  resid = zero
192  RETURN
193  END IF
194 *
195 * Compute the 1-norm of op(A).
196 *
197  IF( lsame( trans, 'N' ) ) THEN
198  anorm = dlantr( '1', uplo, diag, n, n, a, lda, work )
199  ELSE
200  anorm = dlantr( 'I', uplo, diag, n, n, a, lda, work )
201  END IF
202 *
203 * Exit with RESID = 1/EPS if ANORM = 0.
204 *
205  eps = dlamch( 'Epsilon' )
206  IF( anorm.LE.zero ) THEN
207  resid = one / eps
208  RETURN
209  END IF
210 *
211 * Compute the maximum over the number of right hand sides of
212 * norm(op(A)*X - B) / ( norm(op(A)) * norm(X) * EPS )
213 *
214  resid = zero
215  DO 10 j = 1, nrhs
216  CALL dcopy( n, x( 1, j ), 1, work, 1 )
217  CALL dtrmv( uplo, trans, diag, n, a, lda, work, 1 )
218  CALL daxpy( n, -one, b( 1, j ), 1, work, 1 )
219  bnorm = dasum( n, work, 1 )
220  xnorm = dasum( n, x( 1, j ), 1 )
221  IF( xnorm.LE.zero ) THEN
222  resid = one / eps
223  ELSE
224  resid = max( resid, ( ( bnorm / anorm ) / xnorm ) / eps )
225  END IF
226  10 CONTINUE
227 *
228  RETURN
229 *
230 * End of DTRT02
231 *
232  END
subroutine dcopy(N, DX, INCX, DY, INCY)
DCOPY
Definition: dcopy.f:82
subroutine daxpy(N, DA, DX, INCX, DY, INCY)
DAXPY
Definition: daxpy.f:89
subroutine dtrmv(UPLO, TRANS, DIAG, N, A, LDA, X, INCX)
DTRMV
Definition: dtrmv.f:147
subroutine dtrt02(UPLO, TRANS, DIAG, N, NRHS, A, LDA, X, LDX, B, LDB, WORK, RESID)
DTRT02
Definition: dtrt02.f:150