LAPACK  3.10.1
LAPACK: Linear Algebra PACKage
ztrt02.f
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1 *> \brief \b ZTRT02
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 ZTRT02( 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 * DOUBLE PRECISION RESID
18 * ..
19 * .. Array Arguments ..
20 * DOUBLE PRECISION RWORK( * )
21 * COMPLEX*16 A( LDA, * ), B( LDB, * ), WORK( * ),
22 * $ X( LDX, * )
23 * ..
24 *
25 *
26 *> \par Purpose:
27 * =============
28 *>
29 *> \verbatim
30 *>
31 *> ZTRT02 computes the residual for the computed solution to a
32 *> triangular system of linear equations op(A)*X = B, where A is a
33 *> triangular matrix. The test ratio is the maximum over
34 *> norm(b - op(A)*x) / ( ||op(A)||_1 * norm(x) * EPS ),
35 *> where op(A) = A, A**T, or A**H, b is the column of B, x is the
36 *> solution vector, 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**T * X = B (Transpose)
56 *> = 'C': A**H * X = B (Conjugate 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 COMPLEX*16 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 COMPLEX*16 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 COMPLEX*16 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 COMPLEX*16 array, dimension (N)
128 *> \endverbatim
129 *>
130 *> \param[out] RWORK
131 *> \verbatim
132 *> RWORK is DOUBLE PRECISION array, dimension (N)
133 *> \endverbatim
134 *>
135 *> \param[out] RESID
136 *> \verbatim
137 *> RESID is DOUBLE PRECISION
138 *> The maximum over the number of right hand sides of
139 *> norm(op(A)*X - B) / ( norm(op(A)) * norm(X) * EPS ).
140 *> \endverbatim
141 *
142 * Authors:
143 * ========
144 *
145 *> \author Univ. of Tennessee
146 *> \author Univ. of California Berkeley
147 *> \author Univ. of Colorado Denver
148 *> \author NAG Ltd.
149 *
150 *> \ingroup complex16_lin
151 *
152 * =====================================================================
153  SUBROUTINE ztrt02( UPLO, TRANS, DIAG, N, NRHS, A, LDA, X, LDX, B,
154  $ LDB, WORK, RWORK, RESID )
155 *
156 * -- LAPACK test routine --
157 * -- LAPACK is a software package provided by Univ. of Tennessee, --
158 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
159 *
160 * .. Scalar Arguments ..
161  CHARACTER DIAG, TRANS, UPLO
162  INTEGER LDA, LDB, LDX, N, NRHS
163  DOUBLE PRECISION RESID
164 * ..
165 * .. Array Arguments ..
166  DOUBLE PRECISION RWORK( * )
167  COMPLEX*16 A( LDA, * ), B( LDB, * ), WORK( * ),
168  $ x( ldx, * )
169 * ..
170 *
171 * =====================================================================
172 *
173 * .. Parameters ..
174  DOUBLE PRECISION ZERO, ONE
175  parameter( zero = 0.0d+0, one = 1.0d+0 )
176 * ..
177 * .. Local Scalars ..
178  INTEGER J
179  DOUBLE PRECISION ANORM, BNORM, EPS, XNORM
180 * ..
181 * .. External Functions ..
182  LOGICAL LSAME
183  DOUBLE PRECISION DLAMCH, DZASUM, ZLANTR
184  EXTERNAL lsame, dlamch, dzasum, zlantr
185 * ..
186 * .. External Subroutines ..
187  EXTERNAL zaxpy, zcopy, ztrmv
188 * ..
189 * .. Intrinsic Functions ..
190  INTRINSIC dcmplx, max
191 * ..
192 * .. Executable Statements ..
193 *
194 * Quick exit if N = 0 or NRHS = 0
195 *
196  IF( n.LE.0 .OR. nrhs.LE.0 ) THEN
197  resid = zero
198  RETURN
199  END IF
200 *
201 * Compute the 1-norm of op(A).
202 *
203  IF( lsame( trans, 'N' ) ) THEN
204  anorm = zlantr( '1', uplo, diag, n, n, a, lda, rwork )
205  ELSE
206  anorm = zlantr( 'I', uplo, diag, n, n, a, lda, rwork )
207  END IF
208 *
209 * Exit with RESID = 1/EPS if ANORM = 0.
210 *
211  eps = dlamch( 'Epsilon' )
212  IF( anorm.LE.zero ) THEN
213  resid = one / eps
214  RETURN
215  END IF
216 *
217 * Compute the maximum over the number of right hand sides of
218 * norm(op(A)*X - B) / ( norm(op(A)) * norm(X) * EPS )
219 *
220  resid = zero
221  DO 10 j = 1, nrhs
222  CALL zcopy( n, x( 1, j ), 1, work, 1 )
223  CALL ztrmv( uplo, trans, diag, n, a, lda, work, 1 )
224  CALL zaxpy( n, dcmplx( -one ), b( 1, j ), 1, work, 1 )
225  bnorm = dzasum( n, work, 1 )
226  xnorm = dzasum( n, x( 1, j ), 1 )
227  IF( xnorm.LE.zero ) THEN
228  resid = one / eps
229  ELSE
230  resid = max( resid, ( ( bnorm / anorm ) / xnorm ) / eps )
231  END IF
232  10 CONTINUE
233 *
234  RETURN
235 *
236 * End of ZTRT02
237 *
238  END
subroutine zaxpy(N, ZA, ZX, INCX, ZY, INCY)
ZAXPY
Definition: zaxpy.f:88
subroutine zcopy(N, ZX, INCX, ZY, INCY)
ZCOPY
Definition: zcopy.f:81
subroutine ztrmv(UPLO, TRANS, DIAG, N, A, LDA, X, INCX)
ZTRMV
Definition: ztrmv.f:147
subroutine ztrt02(UPLO, TRANS, DIAG, N, NRHS, A, LDA, X, LDX, B, LDB, WORK, RWORK, RESID)
ZTRT02
Definition: ztrt02.f:155