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
245
|
*> \brief \b CPTTS2 solves a tridiagonal system of the form AX=B using the L D LH factorization computed by spttrf.
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
*> \htmlonly
*> Download CPTTS2 + dependencies
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/cptts2.f">
*> [TGZ]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/cptts2.f">
*> [ZIP]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/cptts2.f">
*> [TXT]</a>
*> \endhtmlonly
*
* Definition:
* ===========
*
* SUBROUTINE CPTTS2( IUPLO, N, NRHS, D, E, B, LDB )
*
* .. Scalar Arguments ..
* INTEGER IUPLO, LDB, N, NRHS
* ..
* .. Array Arguments ..
* REAL D( * )
* COMPLEX B( LDB, * ), E( * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> CPTTS2 solves a tridiagonal system of the form
*> A * X = B
*> using the factorization A = U**H*D*U or A = L*D*L**H computed by CPTTRF.
*> D is a diagonal matrix specified in the vector D, U (or L) is a unit
*> bidiagonal matrix whose superdiagonal (subdiagonal) is specified in
*> the vector E, and X and B are N by NRHS matrices.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] IUPLO
*> \verbatim
*> IUPLO is INTEGER
*> Specifies the form of the factorization and whether the
*> vector E is the superdiagonal of the upper bidiagonal factor
*> U or the subdiagonal of the lower bidiagonal factor L.
*> = 1: A = U**H *D*U, E is the superdiagonal of U
*> = 0: A = L*D*L**H, E is the subdiagonal of L
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> The order of the tridiagonal 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] D
*> \verbatim
*> D is REAL array, dimension (N)
*> The n diagonal elements of the diagonal matrix D from the
*> factorization A = U**H *D*U or A = L*D*L**H.
*> \endverbatim
*>
*> \param[in] E
*> \verbatim
*> E is COMPLEX array, dimension (N-1)
*> If IUPLO = 1, the (n-1) superdiagonal elements of the unit
*> bidiagonal factor U from the factorization A = U**H*D*U.
*> If IUPLO = 0, the (n-1) subdiagonal elements of the unit
*> bidiagonal factor L from the factorization A = L*D*L**H.
*> \endverbatim
*>
*> \param[in,out] B
*> \verbatim
*> B is COMPLEX array, dimension (LDB,NRHS)
*> On entry, the right hand side vectors B for the system of
*> linear equations.
*> On exit, the solution vectors, X.
*> \endverbatim
*>
*> \param[in] LDB
*> \verbatim
*> LDB is INTEGER
*> The leading dimension of the array B. LDB >= max(1,N).
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date September 2012
*
*> \ingroup complexPTcomputational
*
* =====================================================================
SUBROUTINE CPTTS2( IUPLO, N, NRHS, D, E, B, LDB )
*
* -- LAPACK computational routine (version 3.4.2) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
* September 2012
*
* .. Scalar Arguments ..
INTEGER IUPLO, LDB, N, NRHS
* ..
* .. Array Arguments ..
REAL D( * )
COMPLEX B( LDB, * ), E( * )
* ..
*
* =====================================================================
*
* .. Local Scalars ..
INTEGER I, J
* ..
* .. External Subroutines ..
EXTERNAL CSSCAL
* ..
* .. Intrinsic Functions ..
INTRINSIC CONJG
* ..
* .. Executable Statements ..
*
* Quick return if possible
*
IF( N.LE.1 ) THEN
IF( N.EQ.1 )
$ CALL CSSCAL( NRHS, 1. / D( 1 ), B, LDB )
RETURN
END IF
*
IF( IUPLO.EQ.1 ) THEN
*
* Solve A * X = B using the factorization A = U**H *D*U,
* overwriting each right hand side vector with its solution.
*
IF( NRHS.LE.2 ) THEN
J = 1
5 CONTINUE
*
* Solve U**H * x = b.
*
DO 10 I = 2, N
B( I, J ) = B( I, J ) - B( I-1, J )*CONJG( E( I-1 ) )
10 CONTINUE
*
* Solve D * U * x = b.
*
DO 20 I = 1, N
B( I, J ) = B( I, J ) / D( I )
20 CONTINUE
DO 30 I = N - 1, 1, -1
B( I, J ) = B( I, J ) - B( I+1, J )*E( I )
30 CONTINUE
IF( J.LT.NRHS ) THEN
J = J + 1
GO TO 5
END IF
ELSE
DO 60 J = 1, NRHS
*
* Solve U**H * x = b.
*
DO 40 I = 2, N
B( I, J ) = B( I, J ) - B( I-1, J )*CONJG( E( I-1 ) )
40 CONTINUE
*
* Solve D * U * x = b.
*
B( N, J ) = B( N, J ) / D( N )
DO 50 I = N - 1, 1, -1
B( I, J ) = B( I, J ) / D( I ) - B( I+1, J )*E( I )
50 CONTINUE
60 CONTINUE
END IF
ELSE
*
* Solve A * X = B using the factorization A = L*D*L**H,
* overwriting each right hand side vector with its solution.
*
IF( NRHS.LE.2 ) THEN
J = 1
65 CONTINUE
*
* Solve L * x = b.
*
DO 70 I = 2, N
B( I, J ) = B( I, J ) - B( I-1, J )*E( I-1 )
70 CONTINUE
*
* Solve D * L**H * x = b.
*
DO 80 I = 1, N
B( I, J ) = B( I, J ) / D( I )
80 CONTINUE
DO 90 I = N - 1, 1, -1
B( I, J ) = B( I, J ) - B( I+1, J )*CONJG( E( I ) )
90 CONTINUE
IF( J.LT.NRHS ) THEN
J = J + 1
GO TO 65
END IF
ELSE
DO 120 J = 1, NRHS
*
* Solve L * x = b.
*
DO 100 I = 2, N
B( I, J ) = B( I, J ) - B( I-1, J )*E( I-1 )
100 CONTINUE
*
* Solve D * L**H * x = b.
*
B( N, J ) = B( N, J ) / D( N )
DO 110 I = N - 1, 1, -1
B( I, J ) = B( I, J ) / D( I ) -
$ B( I+1, J )*CONJG( E( I ) )
110 CONTINUE
120 CONTINUE
END IF
END IF
*
RETURN
*
* End of CPTTS2
*
END
|
