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
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
|
*> \brief \b CTBTRS
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
*> \htmlonly
*> Download CTBTRS + dependencies
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/ctbtrs.f">
*> [TGZ]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/ctbtrs.f">
*> [ZIP]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/ctbtrs.f">
*> [TXT]</a>
*> \endhtmlonly
*
* Definition:
* ===========
*
* SUBROUTINE CTBTRS( UPLO, TRANS, DIAG, N, KD, NRHS, AB, LDAB, B,
* LDB, INFO )
*
* .. Scalar Arguments ..
* CHARACTER DIAG, TRANS, UPLO
* INTEGER INFO, KD, LDAB, LDB, N, NRHS
* ..
* .. Array Arguments ..
* COMPLEX AB( LDAB, * ), B( LDB, * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> CTBTRS solves a triangular system of the form
*>
*> A * X = B, A**T * X = B, or A**H * X = B,
*>
*> where A is a triangular band 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] KD
*> \verbatim
*> KD is INTEGER
*> The number of superdiagonals or subdiagonals of the
*> triangular band matrix A. KD >= 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] AB
*> \verbatim
*> AB is COMPLEX array, dimension (LDAB,N)
*> The upper or lower triangular band matrix A, stored in the
*> first kd+1 rows of AB. The j-th column of A is stored
*> in the j-th column of the array AB as follows:
*> if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
*> if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd).
*> If DIAG = 'U', the diagonal elements of A are not referenced
*> and are assumed to be 1.
*> \endverbatim
*>
*> \param[in] LDAB
*> \verbatim
*> LDAB is INTEGER
*> The leading dimension of the array AB. LDAB >= KD+1.
*> \endverbatim
*>
*> \param[in,out] B
*> \verbatim
*> B is COMPLEX 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 November 2011
*
*> \ingroup complexOTHERcomputational
*
* =====================================================================
SUBROUTINE CTBTRS( UPLO, TRANS, DIAG, N, KD, NRHS, AB, LDAB, B,
$ LDB, INFO )
*
* -- LAPACK computational routine (version 3.4.0) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
* November 2011
*
* .. Scalar Arguments ..
CHARACTER DIAG, TRANS, UPLO
INTEGER INFO, KD, LDAB, LDB, N, NRHS
* ..
* .. Array Arguments ..
COMPLEX AB( LDAB, * ), B( LDB, * )
* ..
*
* =====================================================================
*
* .. Parameters ..
COMPLEX ZERO
PARAMETER ( ZERO = ( 0.0E+0, 0.0E+0 ) )
* ..
* .. Local Scalars ..
LOGICAL NOUNIT, UPPER
INTEGER J
* ..
* .. External Functions ..
LOGICAL LSAME
EXTERNAL LSAME
* ..
* .. External Subroutines ..
EXTERNAL CTBSV, XERBLA
* ..
* .. Intrinsic Functions ..
INTRINSIC MAX
* ..
* .. Executable Statements ..
*
* Test the input parameters.
*
INFO = 0
NOUNIT = LSAME( DIAG, 'N' )
UPPER = LSAME( UPLO, 'U' )
IF( .NOT.UPPER .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( KD.LT.0 ) THEN
INFO = -5
ELSE IF( NRHS.LT.0 ) THEN
INFO = -6
ELSE IF( LDAB.LT.KD+1 ) THEN
INFO = -8
ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
INFO = -10
END IF
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'CTBTRS', -INFO )
RETURN
END IF
*
* Quick return if possible
*
IF( N.EQ.0 )
$ RETURN
*
* Check for singularity.
*
IF( NOUNIT ) THEN
IF( UPPER ) THEN
DO 10 INFO = 1, N
IF( AB( KD+1, INFO ).EQ.ZERO )
$ RETURN
10 CONTINUE
ELSE
DO 20 INFO = 1, N
IF( AB( 1, INFO ).EQ.ZERO )
$ RETURN
20 CONTINUE
END IF
END IF
INFO = 0
*
* Solve A * X = B, A**T * X = B, or A**H * X = B.
*
DO 30 J = 1, NRHS
CALL CTBSV( UPLO, TRANS, DIAG, N, KD, AB, LDAB, B( 1, J ), 1 )
30 CONTINUE
*
RETURN
*
* End of CTBTRS
*
END
|
