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 CGTSV
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
*> \htmlonly
*> Download CGTSV + dependencies
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/cgtsv.f">
*> [TGZ]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/cgtsv.f">
*> [ZIP]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/cgtsv.f">
*> [TXT]</a>
*> \endhtmlonly
*
* Definition:
* ===========
*
* SUBROUTINE CGTSV( N, NRHS, DL, D, DU, B, LDB, INFO )
*
* .. Scalar Arguments ..
* INTEGER INFO, LDB, N, NRHS
* ..
* .. Array Arguments ..
* COMPLEX B( LDB, * ), D( * ), DL( * ), DU( * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> CGTSV solves the equation
*>
*> A*X = B,
*>
*> where A is an N-by-N tridiagonal matrix, by Gaussian elimination with
*> partial pivoting.
*>
*> Note that the equation A**T *X = B may be solved by interchanging the
*> order of the arguments DU and DL.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \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,out] DL
*> \verbatim
*> DL is COMPLEX array, dimension (N-1)
*> On entry, DL must contain the (n-1) subdiagonal elements of
*> A.
*> On exit, DL is overwritten by the (n-2) elements of the
*> second superdiagonal of the upper triangular matrix U from
*> the LU factorization of A, in DL(1), ..., DL(n-2).
*> \endverbatim
*>
*> \param[in,out] D
*> \verbatim
*> D is COMPLEX array, dimension (N)
*> On entry, D must contain the diagonal elements of A.
*> On exit, D is overwritten by the n diagonal elements of U.
*> \endverbatim
*>
*> \param[in,out] DU
*> \verbatim
*> DU is COMPLEX array, dimension (N-1)
*> On entry, DU must contain the (n-1) superdiagonal elements
*> of A.
*> On exit, DU is overwritten by the (n-1) elements of the first
*> superdiagonal of U.
*> \endverbatim
*>
*> \param[in,out] B
*> \verbatim
*> B is COMPLEX array, dimension (LDB,NRHS)
*> On entry, the N-by-NRHS right hand side matrix B.
*> On exit, if INFO = 0, the N-by-NRHS 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, U(i,i) is exactly zero, and the solution
*> has not been computed. The factorization has not been
*> completed unless i = N.
*> \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 CGTSV( N, NRHS, DL, D, DU, B, LDB, INFO )
*
* -- LAPACK computational routine (version 3.3.1) --
* -- 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 ..
INTEGER INFO, LDB, N, NRHS
* ..
* .. Array Arguments ..
COMPLEX B( LDB, * ), D( * ), DL( * ), DU( * )
* ..
*
* =====================================================================
*
* .. Parameters ..
COMPLEX ZERO
PARAMETER ( ZERO = ( 0.0E+0, 0.0E+0 ) )
* ..
* .. Local Scalars ..
INTEGER J, K
COMPLEX MULT, TEMP, ZDUM
* ..
* .. Intrinsic Functions ..
INTRINSIC ABS, AIMAG, MAX, REAL
* ..
* .. External Subroutines ..
EXTERNAL XERBLA
* ..
* .. Statement Functions ..
REAL CABS1
* ..
* .. Statement Function definitions ..
CABS1( ZDUM ) = ABS( REAL( ZDUM ) ) + ABS( AIMAG( ZDUM ) )
* ..
* .. Executable Statements ..
*
INFO = 0
IF( N.LT.0 ) THEN
INFO = -1
ELSE IF( NRHS.LT.0 ) THEN
INFO = -2
ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
INFO = -7
END IF
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'CGTSV ', -INFO )
RETURN
END IF
*
IF( N.EQ.0 )
$ RETURN
*
DO 30 K = 1, N - 1
IF( DL( K ).EQ.ZERO ) THEN
*
* Subdiagonal is zero, no elimination is required.
*
IF( D( K ).EQ.ZERO ) THEN
*
* Diagonal is zero: set INFO = K and return; a unique
* solution can not be found.
*
INFO = K
RETURN
END IF
ELSE IF( CABS1( D( K ) ).GE.CABS1( DL( K ) ) ) THEN
*
* No row interchange required
*
MULT = DL( K ) / D( K )
D( K+1 ) = D( K+1 ) - MULT*DU( K )
DO 10 J = 1, NRHS
B( K+1, J ) = B( K+1, J ) - MULT*B( K, J )
10 CONTINUE
IF( K.LT.( N-1 ) )
$ DL( K ) = ZERO
ELSE
*
* Interchange rows K and K+1
*
MULT = D( K ) / DL( K )
D( K ) = DL( K )
TEMP = D( K+1 )
D( K+1 ) = DU( K ) - MULT*TEMP
IF( K.LT.( N-1 ) ) THEN
DL( K ) = DU( K+1 )
DU( K+1 ) = -MULT*DL( K )
END IF
DU( K ) = TEMP
DO 20 J = 1, NRHS
TEMP = B( K, J )
B( K, J ) = B( K+1, J )
B( K+1, J ) = TEMP - MULT*B( K+1, J )
20 CONTINUE
END IF
30 CONTINUE
IF( D( N ).EQ.ZERO ) THEN
INFO = N
RETURN
END IF
*
* Back solve with the matrix U from the factorization.
*
DO 50 J = 1, NRHS
B( N, J ) = B( N, J ) / D( N )
IF( N.GT.1 )
$ B( N-1, J ) = ( B( N-1, J )-DU( N-1 )*B( N, J ) ) / D( N-1 )
DO 40 K = N - 2, 1, -1
B( K, J ) = ( B( K, J )-DU( K )*B( K+1, J )-DL( K )*
$ B( K+2, J ) ) / D( K )
40 CONTINUE
50 CONTINUE
*
RETURN
*
* End of CGTSV
*
END
|
