1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
|
*> \brief \b ZTRTRS
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
*> \htmlonly
*> Download ZTRTRS + dependencies
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/ztrtrs.f">
*> [TGZ]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/ztrtrs.f">
*> [ZIP]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/ztrtrs.f">
*> [TXT]</a>
*> \endhtmlonly
*
* Definition:
* ===========
*
* SUBROUTINE ZTRTRS( UPLO, TRANS, DIAG, N, NRHS, A, LDA, B, LDB,
* INFO )
*
* .. Scalar Arguments ..
* CHARACTER DIAG, TRANS, UPLO
* INTEGER INFO, LDA, LDB, N, NRHS
* ..
* .. Array Arguments ..
* COMPLEX*16 A( LDA, * ), B( LDB, * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> ZTRTRS solves a triangular system of the form
*>
*> A * X = B, A**T * X = B, or A**H * X = B,
*>
*> where A is a triangular matrix of order N, and B is an N-by-NRHS
*> matrix. A check is made to verify that A is nonsingular.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] UPLO
*> \verbatim
*> UPLO is CHARACTER*1
*> = 'U': A is upper triangular;
*> = 'L': A is lower triangular.
*> \endverbatim
*>
*> \param[in] TRANS
*> \verbatim
*> TRANS is CHARACTER*1
*> Specifies the form of the system of equations:
*> = 'N': A * X = B (No transpose)
*> = 'T': A**T * X = B (Transpose)
*> = 'C': A**H * X = B (Conjugate transpose)
*> \endverbatim
*>
*> \param[in] DIAG
*> \verbatim
*> DIAG is CHARACTER*1
*> = 'N': A is non-unit triangular;
*> = 'U': A is unit triangular.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> The order of the matrix A. N >= 0.
*> \endverbatim
*>
*> \param[in] NRHS
*> \verbatim
*> NRHS is INTEGER
*> The number of right hand sides, i.e., the number of columns
*> of the matrix B. NRHS >= 0.
*> \endverbatim
*>
*> \param[in] A
*> \verbatim
*> A is COMPLEX*16 array, dimension (LDA,N)
*> The triangular matrix A. If UPLO = 'U', the leading N-by-N
*> upper triangular part of the array A contains the upper
*> triangular matrix, and the strictly lower triangular part of
*> A is not referenced. If UPLO = 'L', the leading N-by-N lower
*> triangular part of the array A contains the lower triangular
*> matrix, and the strictly upper triangular part of A is not
*> referenced. If DIAG = 'U', the diagonal elements of A are
*> also not referenced and are assumed to be 1.
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*> LDA is INTEGER
*> The leading dimension of the array A. LDA >= max(1,N).
*> \endverbatim
*>
*> \param[in,out] B
*> \verbatim
*> B is COMPLEX*16 array, dimension (LDB,NRHS)
*> On entry, the right hand side matrix B.
*> On exit, if INFO = 0, the solution matrix X.
*> \endverbatim
*>
*> \param[in] LDB
*> \verbatim
*> LDB is INTEGER
*> The leading dimension of the array B. LDB >= max(1,N).
*> \endverbatim
*>
*> \param[out] INFO
*> \verbatim
*> INFO is INTEGER
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> > 0: if INFO = i, the i-th diagonal element of A is zero,
*> indicating that the matrix is singular and the solutions
*> X have not been computed.
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date December 2016
*
*> \ingroup complex16OTHERcomputational
*
* =====================================================================
SUBROUTINE ZTRTRS( UPLO, TRANS, DIAG, N, NRHS, A, LDA, B, LDB,
$ INFO )
*
* -- LAPACK computational routine (version 3.7.0) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
* December 2016
*
* .. Scalar Arguments ..
CHARACTER DIAG, TRANS, UPLO
INTEGER INFO, LDA, LDB, N, NRHS
* ..
* .. Array Arguments ..
COMPLEX*16 A( LDA, * ), B( LDB, * )
* ..
*
* =====================================================================
*
* .. Parameters ..
COMPLEX*16 ZERO, ONE
PARAMETER ( ZERO = ( 0.0D+0, 0.0D+0 ),
$ ONE = ( 1.0D+0, 0.0D+0 ) )
* ..
* .. Local Scalars ..
LOGICAL NOUNIT
* ..
* .. External Functions ..
LOGICAL LSAME
EXTERNAL LSAME
* ..
* .. External Subroutines ..
EXTERNAL XERBLA, ZTRSM
* ..
* .. Intrinsic Functions ..
INTRINSIC MAX
* ..
* .. Executable Statements ..
*
* Test the input parameters.
*
INFO = 0
NOUNIT = LSAME( DIAG, 'N' )
IF( .NOT.LSAME( UPLO, 'U' ) .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
INFO = -1
ELSE IF( .NOT.LSAME( TRANS, 'N' ) .AND. .NOT.
$ LSAME( TRANS, 'T' ) .AND. .NOT.LSAME( TRANS, 'C' ) ) THEN
INFO = -2
ELSE IF( .NOT.NOUNIT .AND. .NOT.LSAME( DIAG, 'U' ) ) THEN
INFO = -3
ELSE IF( N.LT.0 ) THEN
INFO = -4
ELSE IF( NRHS.LT.0 ) THEN
INFO = -5
ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
INFO = -7
ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
INFO = -9
END IF
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'ZTRTRS', -INFO )
RETURN
END IF
*
* Quick return if possible
*
IF( N.EQ.0 )
$ RETURN
*
* Check for singularity.
*
IF( NOUNIT ) THEN
DO 10 INFO = 1, N
IF( A( INFO, INFO ).EQ.ZERO )
$ RETURN
10 CONTINUE
END IF
INFO = 0
*
* Solve A * x = b, A**T * x = b, or A**H * x = b.
*
CALL ZTRSM( 'Left', UPLO, TRANS, DIAG, N, NRHS, ONE, A, LDA, B,
$ LDB )
*
RETURN
*
* End of ZTRTRS
*
END
|
