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
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
|
*> \brief \b DLAGTM performs a matrix-matrix product of the form C = αAB+βC, where A is a tridiagonal matrix, B and C are rectangular matrices, and α and β are scalars, which may be 0, 1, or -1.
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
*> \htmlonly
*> Download DLAGTM + dependencies
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlagtm.f">
*> [TGZ]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlagtm.f">
*> [ZIP]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlagtm.f">
*> [TXT]</a>
*> \endhtmlonly
*
* Definition:
* ===========
*
* SUBROUTINE DLAGTM( TRANS, N, NRHS, ALPHA, DL, D, DU, X, LDX, BETA,
* B, LDB )
*
* .. Scalar Arguments ..
* CHARACTER TRANS
* INTEGER LDB, LDX, N, NRHS
* DOUBLE PRECISION ALPHA, BETA
* ..
* .. Array Arguments ..
* DOUBLE PRECISION B( LDB, * ), D( * ), DL( * ), DU( * ),
* $ X( LDX, * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> DLAGTM performs a matrix-vector product of the form
*>
*> B := alpha * A * X + beta * B
*>
*> where A is a tridiagonal matrix of order N, B and X are N by NRHS
*> matrices, and alpha and beta are real scalars, each of which may be
*> 0., 1., or -1.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] TRANS
*> \verbatim
*> TRANS is CHARACTER*1
*> Specifies the operation applied to A.
*> = 'N': No transpose, B := alpha * A * X + beta * B
*> = 'T': Transpose, B := alpha * A'* X + beta * B
*> = 'C': Conjugate transpose = Transpose
*> \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 matrices X and B.
*> \endverbatim
*>
*> \param[in] ALPHA
*> \verbatim
*> ALPHA is DOUBLE PRECISION
*> The scalar alpha. ALPHA must be 0., 1., or -1.; otherwise,
*> it is assumed to be 0.
*> \endverbatim
*>
*> \param[in] DL
*> \verbatim
*> DL is DOUBLE PRECISION array, dimension (N-1)
*> The (n-1) sub-diagonal elements of T.
*> \endverbatim
*>
*> \param[in] D
*> \verbatim
*> D is DOUBLE PRECISION array, dimension (N)
*> The diagonal elements of T.
*> \endverbatim
*>
*> \param[in] DU
*> \verbatim
*> DU is DOUBLE PRECISION array, dimension (N-1)
*> The (n-1) super-diagonal elements of T.
*> \endverbatim
*>
*> \param[in] X
*> \verbatim
*> X is DOUBLE PRECISION array, dimension (LDX,NRHS)
*> The N by NRHS matrix X.
*> \endverbatim
*>
*> \param[in] LDX
*> \verbatim
*> LDX is INTEGER
*> The leading dimension of the array X. LDX >= max(N,1).
*> \endverbatim
*>
*> \param[in] BETA
*> \verbatim
*> BETA is DOUBLE PRECISION
*> The scalar beta. BETA must be 0., 1., or -1.; otherwise,
*> it is assumed to be 1.
*> \endverbatim
*>
*> \param[in,out] B
*> \verbatim
*> B is DOUBLE PRECISION array, dimension (LDB,NRHS)
*> On entry, the N by NRHS matrix B.
*> On exit, B is overwritten by the matrix expression
*> B := alpha * A * X + beta * B.
*> \endverbatim
*>
*> \param[in] LDB
*> \verbatim
*> LDB is INTEGER
*> The leading dimension of the array B. LDB >= max(N,1).
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date December 2016
*
*> \ingroup doubleOTHERauxiliary
*
* =====================================================================
SUBROUTINE DLAGTM( TRANS, N, NRHS, ALPHA, DL, D, DU, X, LDX, BETA,
$ B, LDB )
*
* -- LAPACK auxiliary 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 TRANS
INTEGER LDB, LDX, N, NRHS
DOUBLE PRECISION ALPHA, BETA
* ..
* .. Array Arguments ..
DOUBLE PRECISION B( LDB, * ), D( * ), DL( * ), DU( * ),
$ X( LDX, * )
* ..
*
* =====================================================================
*
* .. Parameters ..
DOUBLE PRECISION ONE, ZERO
PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
* ..
* .. Local Scalars ..
INTEGER I, J
* ..
* .. External Functions ..
LOGICAL LSAME
EXTERNAL LSAME
* ..
* .. Executable Statements ..
*
IF( N.EQ.0 )
$ RETURN
*
* Multiply B by BETA if BETA.NE.1.
*
IF( BETA.EQ.ZERO ) THEN
DO 20 J = 1, NRHS
DO 10 I = 1, N
B( I, J ) = ZERO
10 CONTINUE
20 CONTINUE
ELSE IF( BETA.EQ.-ONE ) THEN
DO 40 J = 1, NRHS
DO 30 I = 1, N
B( I, J ) = -B( I, J )
30 CONTINUE
40 CONTINUE
END IF
*
IF( ALPHA.EQ.ONE ) THEN
IF( LSAME( TRANS, 'N' ) ) THEN
*
* Compute B := B + A*X
*
DO 60 J = 1, NRHS
IF( N.EQ.1 ) THEN
B( 1, J ) = B( 1, J ) + D( 1 )*X( 1, J )
ELSE
B( 1, J ) = B( 1, J ) + D( 1 )*X( 1, J ) +
$ DU( 1 )*X( 2, J )
B( N, J ) = B( N, J ) + DL( N-1 )*X( N-1, J ) +
$ D( N )*X( N, J )
DO 50 I = 2, N - 1
B( I, J ) = B( I, J ) + DL( I-1 )*X( I-1, J ) +
$ D( I )*X( I, J ) + DU( I )*X( I+1, J )
50 CONTINUE
END IF
60 CONTINUE
ELSE
*
* Compute B := B + A**T*X
*
DO 80 J = 1, NRHS
IF( N.EQ.1 ) THEN
B( 1, J ) = B( 1, J ) + D( 1 )*X( 1, J )
ELSE
B( 1, J ) = B( 1, J ) + D( 1 )*X( 1, J ) +
$ DL( 1 )*X( 2, J )
B( N, J ) = B( N, J ) + DU( N-1 )*X( N-1, J ) +
$ D( N )*X( N, J )
DO 70 I = 2, N - 1
B( I, J ) = B( I, J ) + DU( I-1 )*X( I-1, J ) +
$ D( I )*X( I, J ) + DL( I )*X( I+1, J )
70 CONTINUE
END IF
80 CONTINUE
END IF
ELSE IF( ALPHA.EQ.-ONE ) THEN
IF( LSAME( TRANS, 'N' ) ) THEN
*
* Compute B := B - A*X
*
DO 100 J = 1, NRHS
IF( N.EQ.1 ) THEN
B( 1, J ) = B( 1, J ) - D( 1 )*X( 1, J )
ELSE
B( 1, J ) = B( 1, J ) - D( 1 )*X( 1, J ) -
$ DU( 1 )*X( 2, J )
B( N, J ) = B( N, J ) - DL( N-1 )*X( N-1, J ) -
$ D( N )*X( N, J )
DO 90 I = 2, N - 1
B( I, J ) = B( I, J ) - DL( I-1 )*X( I-1, J ) -
$ D( I )*X( I, J ) - DU( I )*X( I+1, J )
90 CONTINUE
END IF
100 CONTINUE
ELSE
*
* Compute B := B - A**T*X
*
DO 120 J = 1, NRHS
IF( N.EQ.1 ) THEN
B( 1, J ) = B( 1, J ) - D( 1 )*X( 1, J )
ELSE
B( 1, J ) = B( 1, J ) - D( 1 )*X( 1, J ) -
$ DL( 1 )*X( 2, J )
B( N, J ) = B( N, J ) - DU( N-1 )*X( N-1, J ) -
$ D( N )*X( N, J )
DO 110 I = 2, N - 1
B( I, J ) = B( I, J ) - DU( I-1 )*X( I-1, J ) -
$ D( I )*X( I, J ) - DL( I )*X( I+1, J )
110 CONTINUE
END IF
120 CONTINUE
END IF
END IF
RETURN
*
* End of DLAGTM
*
END
|
