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
|
SUBROUTINE DLAGTM( TRANS, N, NRHS, ALPHA, DL, D, DU, X, LDX, BETA,
$ B, LDB )
*
* -- LAPACK auxiliary routine (version 2.0) --
* Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
* Courant Institute, Argonne National Lab, and Rice University
* October 31, 1992
*
* .. Scalar Arguments ..
CHARACTER TRANS
INTEGER LDB, LDX, N, NRHS
DOUBLE PRECISION ALPHA, BETA
* ..
* .. Array Arguments ..
DOUBLE PRECISION B( LDB, * ), D( * ), DL( * ), DU( * ),
$ X( LDX, * )
* ..
*
* Purpose
* =======
*
* 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.
*
* Arguments
* =========
*
* TRANS (input) CHARACTER
* 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
*
* N (input) INTEGER
* The order of the matrix A. N >= 0.
*
* NRHS (input) INTEGER
* The number of right hand sides, i.e., the number of columns
* of the matrices X and B.
*
* ALPHA (input) DOUBLE PRECISION
* The scalar alpha. ALPHA must be 0., 1., or -1.; otherwise,
* it is assumed to be 0.
*
* DL (input) DOUBLE PRECISION array, dimension (N-1)
* The (n-1) sub-diagonal elements of T.
*
* D (input) DOUBLE PRECISION array, dimension (N)
* The diagonal elements of T.
*
* DU (input) DOUBLE PRECISION array, dimension (N-1)
* The (n-1) super-diagonal elements of T.
*
* X (input) DOUBLE PRECISION array, dimension (LDX,NRHS)
* The N by NRHS matrix X.
* LDX (input) INTEGER
* The leading dimension of the array X. LDX >= max(N,1).
*
* BETA (input) DOUBLE PRECISION
* The scalar beta. BETA must be 0., 1., or -1.; otherwise,
* it is assumed to be 1.
*
* B (input/output) 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.
*
* LDB (input) INTEGER
* The leading dimension of the array B. LDB >= max(N,1).
*
* =====================================================================
*
* .. 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'*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'*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
|
