1 SUBROUTINE DLAGTM( TRANS, N, NRHS, ALPHA, DL, D, DU, X, LDX, BETA,
2 $ B, LDB )
3 *
4 * -- LAPACK auxiliary routine (version 3.3.1) --
5 * -- LAPACK is a software package provided by Univ. of Tennessee, --
6 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
7 * -- April 2011 --
8 *
9 * .. Scalar Arguments ..
10 CHARACTER TRANS
11 INTEGER LDB, LDX, N, NRHS
12 DOUBLE PRECISION ALPHA, BETA
13 * ..
14 * .. Array Arguments ..
15 DOUBLE PRECISION B( LDB, * ), D( * ), DL( * ), DU( * ),
16 $ X( LDX, * )
17 * ..
18 *
19 * Purpose
20 * =======
21 *
22 * DLAGTM performs a matrix-vector product of the form
23 *
24 * B := alpha * A * X + beta * B
25 *
26 * where A is a tridiagonal matrix of order N, B and X are N by NRHS
27 * matrices, and alpha and beta are real scalars, each of which may be
28 * 0., 1., or -1.
29 *
30 * Arguments
31 * =========
32 *
33 * TRANS (input) CHARACTER*1
34 * Specifies the operation applied to A.
35 * = 'N': No transpose, B := alpha * A * X + beta * B
36 * = 'T': Transpose, B := alpha * A'* X + beta * B
37 * = 'C': Conjugate transpose = Transpose
38 *
39 * N (input) INTEGER
40 * The order of the matrix A. N >= 0.
41 *
42 * NRHS (input) INTEGER
43 * The number of right hand sides, i.e., the number of columns
44 * of the matrices X and B.
45 *
46 * ALPHA (input) DOUBLE PRECISION
47 * The scalar alpha. ALPHA must be 0., 1., or -1.; otherwise,
48 * it is assumed to be 0.
49 *
50 * DL (input) DOUBLE PRECISION array, dimension (N-1)
51 * The (n-1) sub-diagonal elements of T.
52 *
53 * D (input) DOUBLE PRECISION array, dimension (N)
54 * The diagonal elements of T.
55 *
56 * DU (input) DOUBLE PRECISION array, dimension (N-1)
57 * The (n-1) super-diagonal elements of T.
58 *
59 * X (input) DOUBLE PRECISION array, dimension (LDX,NRHS)
60 * The N by NRHS matrix X.
61 * LDX (input) INTEGER
62 * The leading dimension of the array X. LDX >= max(N,1).
63 *
64 * BETA (input) DOUBLE PRECISION
65 * The scalar beta. BETA must be 0., 1., or -1.; otherwise,
66 * it is assumed to be 1.
67 *
68 * B (input/output) DOUBLE PRECISION array, dimension (LDB,NRHS)
69 * On entry, the N by NRHS matrix B.
70 * On exit, B is overwritten by the matrix expression
71 * B := alpha * A * X + beta * B.
72 *
73 * LDB (input) INTEGER
74 * The leading dimension of the array B. LDB >= max(N,1).
75 *
76 * =====================================================================
77 *
78 * .. Parameters ..
79 DOUBLE PRECISION ONE, ZERO
80 PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
81 * ..
82 * .. Local Scalars ..
83 INTEGER I, J
84 * ..
85 * .. External Functions ..
86 LOGICAL LSAME
87 EXTERNAL LSAME
88 * ..
89 * .. Executable Statements ..
90 *
91 IF( N.EQ.0 )
92 $ RETURN
93 *
94 * Multiply B by BETA if BETA.NE.1.
95 *
96 IF( BETA.EQ.ZERO ) THEN
97 DO 20 J = 1, NRHS
98 DO 10 I = 1, N
99 B( I, J ) = ZERO
100 10 CONTINUE
101 20 CONTINUE
102 ELSE IF( BETA.EQ.-ONE ) THEN
103 DO 40 J = 1, NRHS
104 DO 30 I = 1, N
105 B( I, J ) = -B( I, J )
106 30 CONTINUE
107 40 CONTINUE
108 END IF
109 *
110 IF( ALPHA.EQ.ONE ) THEN
111 IF( LSAME( TRANS, 'N' ) ) THEN
112 *
113 * Compute B := B + A*X
114 *
115 DO 60 J = 1, NRHS
116 IF( N.EQ.1 ) THEN
117 B( 1, J ) = B( 1, J ) + D( 1 )*X( 1, J )
118 ELSE
119 B( 1, J ) = B( 1, J ) + D( 1 )*X( 1, J ) +
120 $ DU( 1 )*X( 2, J )
121 B( N, J ) = B( N, J ) + DL( N-1 )*X( N-1, J ) +
122 $ D( N )*X( N, J )
123 DO 50 I = 2, N - 1
124 B( I, J ) = B( I, J ) + DL( I-1 )*X( I-1, J ) +
125 $ D( I )*X( I, J ) + DU( I )*X( I+1, J )
126 50 CONTINUE
127 END IF
128 60 CONTINUE
129 ELSE
130 *
131 * Compute B := B + A**T*X
132 *
133 DO 80 J = 1, NRHS
134 IF( N.EQ.1 ) THEN
135 B( 1, J ) = B( 1, J ) + D( 1 )*X( 1, J )
136 ELSE
137 B( 1, J ) = B( 1, J ) + D( 1 )*X( 1, J ) +
138 $ DL( 1 )*X( 2, J )
139 B( N, J ) = B( N, J ) + DU( N-1 )*X( N-1, J ) +
140 $ D( N )*X( N, J )
141 DO 70 I = 2, N - 1
142 B( I, J ) = B( I, J ) + DU( I-1 )*X( I-1, J ) +
143 $ D( I )*X( I, J ) + DL( I )*X( I+1, J )
144 70 CONTINUE
145 END IF
146 80 CONTINUE
147 END IF
148 ELSE IF( ALPHA.EQ.-ONE ) THEN
149 IF( LSAME( TRANS, 'N' ) ) THEN
150 *
151 * Compute B := B - A*X
152 *
153 DO 100 J = 1, NRHS
154 IF( N.EQ.1 ) THEN
155 B( 1, J ) = B( 1, J ) - D( 1 )*X( 1, J )
156 ELSE
157 B( 1, J ) = B( 1, J ) - D( 1 )*X( 1, J ) -
158 $ DU( 1 )*X( 2, J )
159 B( N, J ) = B( N, J ) - DL( N-1 )*X( N-1, J ) -
160 $ D( N )*X( N, J )
161 DO 90 I = 2, N - 1
162 B( I, J ) = B( I, J ) - DL( I-1 )*X( I-1, J ) -
163 $ D( I )*X( I, J ) - DU( I )*X( I+1, J )
164 90 CONTINUE
165 END IF
166 100 CONTINUE
167 ELSE
168 *
169 * Compute B := B - A**T*X
170 *
171 DO 120 J = 1, NRHS
172 IF( N.EQ.1 ) THEN
173 B( 1, J ) = B( 1, J ) - D( 1 )*X( 1, J )
174 ELSE
175 B( 1, J ) = B( 1, J ) - D( 1 )*X( 1, J ) -
176 $ DL( 1 )*X( 2, J )
177 B( N, J ) = B( N, J ) - DU( N-1 )*X( N-1, J ) -
178 $ D( N )*X( N, J )
179 DO 110 I = 2, N - 1
180 B( I, J ) = B( I, J ) - DU( I-1 )*X( I-1, J ) -
181 $ D( I )*X( I, J ) - DL( I )*X( I+1, J )
182 110 CONTINUE
183 END IF
184 120 CONTINUE
185 END IF
186 END IF
187 RETURN
188 *
189 * End of DLAGTM
190 *
191 END
2 $ B, LDB )
3 *
4 * -- LAPACK auxiliary routine (version 3.3.1) --
5 * -- LAPACK is a software package provided by Univ. of Tennessee, --
6 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
7 * -- April 2011 --
8 *
9 * .. Scalar Arguments ..
10 CHARACTER TRANS
11 INTEGER LDB, LDX, N, NRHS
12 DOUBLE PRECISION ALPHA, BETA
13 * ..
14 * .. Array Arguments ..
15 DOUBLE PRECISION B( LDB, * ), D( * ), DL( * ), DU( * ),
16 $ X( LDX, * )
17 * ..
18 *
19 * Purpose
20 * =======
21 *
22 * DLAGTM performs a matrix-vector product of the form
23 *
24 * B := alpha * A * X + beta * B
25 *
26 * where A is a tridiagonal matrix of order N, B and X are N by NRHS
27 * matrices, and alpha and beta are real scalars, each of which may be
28 * 0., 1., or -1.
29 *
30 * Arguments
31 * =========
32 *
33 * TRANS (input) CHARACTER*1
34 * Specifies the operation applied to A.
35 * = 'N': No transpose, B := alpha * A * X + beta * B
36 * = 'T': Transpose, B := alpha * A'* X + beta * B
37 * = 'C': Conjugate transpose = Transpose
38 *
39 * N (input) INTEGER
40 * The order of the matrix A. N >= 0.
41 *
42 * NRHS (input) INTEGER
43 * The number of right hand sides, i.e., the number of columns
44 * of the matrices X and B.
45 *
46 * ALPHA (input) DOUBLE PRECISION
47 * The scalar alpha. ALPHA must be 0., 1., or -1.; otherwise,
48 * it is assumed to be 0.
49 *
50 * DL (input) DOUBLE PRECISION array, dimension (N-1)
51 * The (n-1) sub-diagonal elements of T.
52 *
53 * D (input) DOUBLE PRECISION array, dimension (N)
54 * The diagonal elements of T.
55 *
56 * DU (input) DOUBLE PRECISION array, dimension (N-1)
57 * The (n-1) super-diagonal elements of T.
58 *
59 * X (input) DOUBLE PRECISION array, dimension (LDX,NRHS)
60 * The N by NRHS matrix X.
61 * LDX (input) INTEGER
62 * The leading dimension of the array X. LDX >= max(N,1).
63 *
64 * BETA (input) DOUBLE PRECISION
65 * The scalar beta. BETA must be 0., 1., or -1.; otherwise,
66 * it is assumed to be 1.
67 *
68 * B (input/output) DOUBLE PRECISION array, dimension (LDB,NRHS)
69 * On entry, the N by NRHS matrix B.
70 * On exit, B is overwritten by the matrix expression
71 * B := alpha * A * X + beta * B.
72 *
73 * LDB (input) INTEGER
74 * The leading dimension of the array B. LDB >= max(N,1).
75 *
76 * =====================================================================
77 *
78 * .. Parameters ..
79 DOUBLE PRECISION ONE, ZERO
80 PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
81 * ..
82 * .. Local Scalars ..
83 INTEGER I, J
84 * ..
85 * .. External Functions ..
86 LOGICAL LSAME
87 EXTERNAL LSAME
88 * ..
89 * .. Executable Statements ..
90 *
91 IF( N.EQ.0 )
92 $ RETURN
93 *
94 * Multiply B by BETA if BETA.NE.1.
95 *
96 IF( BETA.EQ.ZERO ) THEN
97 DO 20 J = 1, NRHS
98 DO 10 I = 1, N
99 B( I, J ) = ZERO
100 10 CONTINUE
101 20 CONTINUE
102 ELSE IF( BETA.EQ.-ONE ) THEN
103 DO 40 J = 1, NRHS
104 DO 30 I = 1, N
105 B( I, J ) = -B( I, J )
106 30 CONTINUE
107 40 CONTINUE
108 END IF
109 *
110 IF( ALPHA.EQ.ONE ) THEN
111 IF( LSAME( TRANS, 'N' ) ) THEN
112 *
113 * Compute B := B + A*X
114 *
115 DO 60 J = 1, NRHS
116 IF( N.EQ.1 ) THEN
117 B( 1, J ) = B( 1, J ) + D( 1 )*X( 1, J )
118 ELSE
119 B( 1, J ) = B( 1, J ) + D( 1 )*X( 1, J ) +
120 $ DU( 1 )*X( 2, J )
121 B( N, J ) = B( N, J ) + DL( N-1 )*X( N-1, J ) +
122 $ D( N )*X( N, J )
123 DO 50 I = 2, N - 1
124 B( I, J ) = B( I, J ) + DL( I-1 )*X( I-1, J ) +
125 $ D( I )*X( I, J ) + DU( I )*X( I+1, J )
126 50 CONTINUE
127 END IF
128 60 CONTINUE
129 ELSE
130 *
131 * Compute B := B + A**T*X
132 *
133 DO 80 J = 1, NRHS
134 IF( N.EQ.1 ) THEN
135 B( 1, J ) = B( 1, J ) + D( 1 )*X( 1, J )
136 ELSE
137 B( 1, J ) = B( 1, J ) + D( 1 )*X( 1, J ) +
138 $ DL( 1 )*X( 2, J )
139 B( N, J ) = B( N, J ) + DU( N-1 )*X( N-1, J ) +
140 $ D( N )*X( N, J )
141 DO 70 I = 2, N - 1
142 B( I, J ) = B( I, J ) + DU( I-1 )*X( I-1, J ) +
143 $ D( I )*X( I, J ) + DL( I )*X( I+1, J )
144 70 CONTINUE
145 END IF
146 80 CONTINUE
147 END IF
148 ELSE IF( ALPHA.EQ.-ONE ) THEN
149 IF( LSAME( TRANS, 'N' ) ) THEN
150 *
151 * Compute B := B - A*X
152 *
153 DO 100 J = 1, NRHS
154 IF( N.EQ.1 ) THEN
155 B( 1, J ) = B( 1, J ) - D( 1 )*X( 1, J )
156 ELSE
157 B( 1, J ) = B( 1, J ) - D( 1 )*X( 1, J ) -
158 $ DU( 1 )*X( 2, J )
159 B( N, J ) = B( N, J ) - DL( N-1 )*X( N-1, J ) -
160 $ D( N )*X( N, J )
161 DO 90 I = 2, N - 1
162 B( I, J ) = B( I, J ) - DL( I-1 )*X( I-1, J ) -
163 $ D( I )*X( I, J ) - DU( I )*X( I+1, J )
164 90 CONTINUE
165 END IF
166 100 CONTINUE
167 ELSE
168 *
169 * Compute B := B - A**T*X
170 *
171 DO 120 J = 1, NRHS
172 IF( N.EQ.1 ) THEN
173 B( 1, J ) = B( 1, J ) - D( 1 )*X( 1, J )
174 ELSE
175 B( 1, J ) = B( 1, J ) - D( 1 )*X( 1, J ) -
176 $ DL( 1 )*X( 2, J )
177 B( N, J ) = B( N, J ) - DU( N-1 )*X( N-1, J ) -
178 $ D( N )*X( N, J )
179 DO 110 I = 2, N - 1
180 B( I, J ) = B( I, J ) - DU( I-1 )*X( I-1, J ) -
181 $ D( I )*X( I, J ) - DL( I )*X( I+1, J )
182 110 CONTINUE
183 END IF
184 120 CONTINUE
185 END IF
186 END IF
187 RETURN
188 *
189 * End of DLAGTM
190 *
191 END