1 SUBROUTINE ZLAGTM( 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 COMPLEX*16 B( LDB, * ), D( * ), DL( * ), DU( * ),
16 $ X( LDX, * )
17 * ..
18 *
19 * Purpose
20 * =======
21 *
22 * ZLAGTM 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**T * X + beta * B
37 * = 'C': Conjugate transpose, B := alpha * A**H * X + beta * B
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) COMPLEX*16 array, dimension (N-1)
51 * The (n-1) sub-diagonal elements of T.
52 *
53 * D (input) COMPLEX*16 array, dimension (N)
54 * The diagonal elements of T.
55 *
56 * DU (input) COMPLEX*16 array, dimension (N-1)
57 * The (n-1) super-diagonal elements of T.
58 *
59 * X (input) COMPLEX*16 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) COMPLEX*16 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 * .. Intrinsic Functions ..
90 INTRINSIC DCONJG
91 * ..
92 * .. Executable Statements ..
93 *
94 IF( N.EQ.0 )
95 $ RETURN
96 *
97 * Multiply B by BETA if BETA.NE.1.
98 *
99 IF( BETA.EQ.ZERO ) THEN
100 DO 20 J = 1, NRHS
101 DO 10 I = 1, N
102 B( I, J ) = ZERO
103 10 CONTINUE
104 20 CONTINUE
105 ELSE IF( BETA.EQ.-ONE ) THEN
106 DO 40 J = 1, NRHS
107 DO 30 I = 1, N
108 B( I, J ) = -B( I, J )
109 30 CONTINUE
110 40 CONTINUE
111 END IF
112 *
113 IF( ALPHA.EQ.ONE ) THEN
114 IF( LSAME( TRANS, 'N' ) ) THEN
115 *
116 * Compute B := B + A*X
117 *
118 DO 60 J = 1, NRHS
119 IF( N.EQ.1 ) THEN
120 B( 1, J ) = B( 1, J ) + D( 1 )*X( 1, J )
121 ELSE
122 B( 1, J ) = B( 1, J ) + D( 1 )*X( 1, J ) +
123 $ DU( 1 )*X( 2, J )
124 B( N, J ) = B( N, J ) + DL( N-1 )*X( N-1, J ) +
125 $ D( N )*X( N, J )
126 DO 50 I = 2, N - 1
127 B( I, J ) = B( I, J ) + DL( I-1 )*X( I-1, J ) +
128 $ D( I )*X( I, J ) + DU( I )*X( I+1, J )
129 50 CONTINUE
130 END IF
131 60 CONTINUE
132 ELSE IF( LSAME( TRANS, 'T' ) ) THEN
133 *
134 * Compute B := B + A**T * X
135 *
136 DO 80 J = 1, NRHS
137 IF( N.EQ.1 ) THEN
138 B( 1, J ) = B( 1, J ) + D( 1 )*X( 1, J )
139 ELSE
140 B( 1, J ) = B( 1, J ) + D( 1 )*X( 1, J ) +
141 $ DL( 1 )*X( 2, J )
142 B( N, J ) = B( N, J ) + DU( N-1 )*X( N-1, J ) +
143 $ D( N )*X( N, J )
144 DO 70 I = 2, N - 1
145 B( I, J ) = B( I, J ) + DU( I-1 )*X( I-1, J ) +
146 $ D( I )*X( I, J ) + DL( I )*X( I+1, J )
147 70 CONTINUE
148 END IF
149 80 CONTINUE
150 ELSE IF( LSAME( TRANS, 'C' ) ) THEN
151 *
152 * Compute B := B + A**H * X
153 *
154 DO 100 J = 1, NRHS
155 IF( N.EQ.1 ) THEN
156 B( 1, J ) = B( 1, J ) + DCONJG( D( 1 ) )*X( 1, J )
157 ELSE
158 B( 1, J ) = B( 1, J ) + DCONJG( D( 1 ) )*X( 1, J ) +
159 $ DCONJG( DL( 1 ) )*X( 2, J )
160 B( N, J ) = B( N, J ) + DCONJG( DU( N-1 ) )*
161 $ X( N-1, J ) + DCONJG( D( N ) )*X( N, J )
162 DO 90 I = 2, N - 1
163 B( I, J ) = B( I, J ) + DCONJG( DU( I-1 ) )*
164 $ X( I-1, J ) + DCONJG( D( I ) )*
165 $ X( I, J ) + DCONJG( DL( I ) )*
166 $ X( I+1, J )
167 90 CONTINUE
168 END IF
169 100 CONTINUE
170 END IF
171 ELSE IF( ALPHA.EQ.-ONE ) THEN
172 IF( LSAME( TRANS, 'N' ) ) THEN
173 *
174 * Compute B := B - A*X
175 *
176 DO 120 J = 1, NRHS
177 IF( N.EQ.1 ) THEN
178 B( 1, J ) = B( 1, J ) - D( 1 )*X( 1, J )
179 ELSE
180 B( 1, J ) = B( 1, J ) - D( 1 )*X( 1, J ) -
181 $ DU( 1 )*X( 2, J )
182 B( N, J ) = B( N, J ) - DL( N-1 )*X( N-1, J ) -
183 $ D( N )*X( N, J )
184 DO 110 I = 2, N - 1
185 B( I, J ) = B( I, J ) - DL( I-1 )*X( I-1, J ) -
186 $ D( I )*X( I, J ) - DU( I )*X( I+1, J )
187 110 CONTINUE
188 END IF
189 120 CONTINUE
190 ELSE IF( LSAME( TRANS, 'T' ) ) THEN
191 *
192 * Compute B := B - A**T *X
193 *
194 DO 140 J = 1, NRHS
195 IF( N.EQ.1 ) THEN
196 B( 1, J ) = B( 1, J ) - D( 1 )*X( 1, J )
197 ELSE
198 B( 1, J ) = B( 1, J ) - D( 1 )*X( 1, J ) -
199 $ DL( 1 )*X( 2, J )
200 B( N, J ) = B( N, J ) - DU( N-1 )*X( N-1, J ) -
201 $ D( N )*X( N, J )
202 DO 130 I = 2, N - 1
203 B( I, J ) = B( I, J ) - DU( I-1 )*X( I-1, J ) -
204 $ D( I )*X( I, J ) - DL( I )*X( I+1, J )
205 130 CONTINUE
206 END IF
207 140 CONTINUE
208 ELSE IF( LSAME( TRANS, 'C' ) ) THEN
209 *
210 * Compute B := B - A**H *X
211 *
212 DO 160 J = 1, NRHS
213 IF( N.EQ.1 ) THEN
214 B( 1, J ) = B( 1, J ) - DCONJG( D( 1 ) )*X( 1, J )
215 ELSE
216 B( 1, J ) = B( 1, J ) - DCONJG( D( 1 ) )*X( 1, J ) -
217 $ DCONJG( DL( 1 ) )*X( 2, J )
218 B( N, J ) = B( N, J ) - DCONJG( DU( N-1 ) )*
219 $ X( N-1, J ) - DCONJG( D( N ) )*X( N, J )
220 DO 150 I = 2, N - 1
221 B( I, J ) = B( I, J ) - DCONJG( DU( I-1 ) )*
222 $ X( I-1, J ) - DCONJG( D( I ) )*
223 $ X( I, J ) - DCONJG( DL( I ) )*
224 $ X( I+1, J )
225 150 CONTINUE
226 END IF
227 160 CONTINUE
228 END IF
229 END IF
230 RETURN
231 *
232 * End of ZLAGTM
233 *
234 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 COMPLEX*16 B( LDB, * ), D( * ), DL( * ), DU( * ),
16 $ X( LDX, * )
17 * ..
18 *
19 * Purpose
20 * =======
21 *
22 * ZLAGTM 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**T * X + beta * B
37 * = 'C': Conjugate transpose, B := alpha * A**H * X + beta * B
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) COMPLEX*16 array, dimension (N-1)
51 * The (n-1) sub-diagonal elements of T.
52 *
53 * D (input) COMPLEX*16 array, dimension (N)
54 * The diagonal elements of T.
55 *
56 * DU (input) COMPLEX*16 array, dimension (N-1)
57 * The (n-1) super-diagonal elements of T.
58 *
59 * X (input) COMPLEX*16 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) COMPLEX*16 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 * .. Intrinsic Functions ..
90 INTRINSIC DCONJG
91 * ..
92 * .. Executable Statements ..
93 *
94 IF( N.EQ.0 )
95 $ RETURN
96 *
97 * Multiply B by BETA if BETA.NE.1.
98 *
99 IF( BETA.EQ.ZERO ) THEN
100 DO 20 J = 1, NRHS
101 DO 10 I = 1, N
102 B( I, J ) = ZERO
103 10 CONTINUE
104 20 CONTINUE
105 ELSE IF( BETA.EQ.-ONE ) THEN
106 DO 40 J = 1, NRHS
107 DO 30 I = 1, N
108 B( I, J ) = -B( I, J )
109 30 CONTINUE
110 40 CONTINUE
111 END IF
112 *
113 IF( ALPHA.EQ.ONE ) THEN
114 IF( LSAME( TRANS, 'N' ) ) THEN
115 *
116 * Compute B := B + A*X
117 *
118 DO 60 J = 1, NRHS
119 IF( N.EQ.1 ) THEN
120 B( 1, J ) = B( 1, J ) + D( 1 )*X( 1, J )
121 ELSE
122 B( 1, J ) = B( 1, J ) + D( 1 )*X( 1, J ) +
123 $ DU( 1 )*X( 2, J )
124 B( N, J ) = B( N, J ) + DL( N-1 )*X( N-1, J ) +
125 $ D( N )*X( N, J )
126 DO 50 I = 2, N - 1
127 B( I, J ) = B( I, J ) + DL( I-1 )*X( I-1, J ) +
128 $ D( I )*X( I, J ) + DU( I )*X( I+1, J )
129 50 CONTINUE
130 END IF
131 60 CONTINUE
132 ELSE IF( LSAME( TRANS, 'T' ) ) THEN
133 *
134 * Compute B := B + A**T * X
135 *
136 DO 80 J = 1, NRHS
137 IF( N.EQ.1 ) THEN
138 B( 1, J ) = B( 1, J ) + D( 1 )*X( 1, J )
139 ELSE
140 B( 1, J ) = B( 1, J ) + D( 1 )*X( 1, J ) +
141 $ DL( 1 )*X( 2, J )
142 B( N, J ) = B( N, J ) + DU( N-1 )*X( N-1, J ) +
143 $ D( N )*X( N, J )
144 DO 70 I = 2, N - 1
145 B( I, J ) = B( I, J ) + DU( I-1 )*X( I-1, J ) +
146 $ D( I )*X( I, J ) + DL( I )*X( I+1, J )
147 70 CONTINUE
148 END IF
149 80 CONTINUE
150 ELSE IF( LSAME( TRANS, 'C' ) ) THEN
151 *
152 * Compute B := B + A**H * X
153 *
154 DO 100 J = 1, NRHS
155 IF( N.EQ.1 ) THEN
156 B( 1, J ) = B( 1, J ) + DCONJG( D( 1 ) )*X( 1, J )
157 ELSE
158 B( 1, J ) = B( 1, J ) + DCONJG( D( 1 ) )*X( 1, J ) +
159 $ DCONJG( DL( 1 ) )*X( 2, J )
160 B( N, J ) = B( N, J ) + DCONJG( DU( N-1 ) )*
161 $ X( N-1, J ) + DCONJG( D( N ) )*X( N, J )
162 DO 90 I = 2, N - 1
163 B( I, J ) = B( I, J ) + DCONJG( DU( I-1 ) )*
164 $ X( I-1, J ) + DCONJG( D( I ) )*
165 $ X( I, J ) + DCONJG( DL( I ) )*
166 $ X( I+1, J )
167 90 CONTINUE
168 END IF
169 100 CONTINUE
170 END IF
171 ELSE IF( ALPHA.EQ.-ONE ) THEN
172 IF( LSAME( TRANS, 'N' ) ) THEN
173 *
174 * Compute B := B - A*X
175 *
176 DO 120 J = 1, NRHS
177 IF( N.EQ.1 ) THEN
178 B( 1, J ) = B( 1, J ) - D( 1 )*X( 1, J )
179 ELSE
180 B( 1, J ) = B( 1, J ) - D( 1 )*X( 1, J ) -
181 $ DU( 1 )*X( 2, J )
182 B( N, J ) = B( N, J ) - DL( N-1 )*X( N-1, J ) -
183 $ D( N )*X( N, J )
184 DO 110 I = 2, N - 1
185 B( I, J ) = B( I, J ) - DL( I-1 )*X( I-1, J ) -
186 $ D( I )*X( I, J ) - DU( I )*X( I+1, J )
187 110 CONTINUE
188 END IF
189 120 CONTINUE
190 ELSE IF( LSAME( TRANS, 'T' ) ) THEN
191 *
192 * Compute B := B - A**T *X
193 *
194 DO 140 J = 1, NRHS
195 IF( N.EQ.1 ) THEN
196 B( 1, J ) = B( 1, J ) - D( 1 )*X( 1, J )
197 ELSE
198 B( 1, J ) = B( 1, J ) - D( 1 )*X( 1, J ) -
199 $ DL( 1 )*X( 2, J )
200 B( N, J ) = B( N, J ) - DU( N-1 )*X( N-1, J ) -
201 $ D( N )*X( N, J )
202 DO 130 I = 2, N - 1
203 B( I, J ) = B( I, J ) - DU( I-1 )*X( I-1, J ) -
204 $ D( I )*X( I, J ) - DL( I )*X( I+1, J )
205 130 CONTINUE
206 END IF
207 140 CONTINUE
208 ELSE IF( LSAME( TRANS, 'C' ) ) THEN
209 *
210 * Compute B := B - A**H *X
211 *
212 DO 160 J = 1, NRHS
213 IF( N.EQ.1 ) THEN
214 B( 1, J ) = B( 1, J ) - DCONJG( D( 1 ) )*X( 1, J )
215 ELSE
216 B( 1, J ) = B( 1, J ) - DCONJG( D( 1 ) )*X( 1, J ) -
217 $ DCONJG( DL( 1 ) )*X( 2, J )
218 B( N, J ) = B( N, J ) - DCONJG( DU( N-1 ) )*
219 $ X( N-1, J ) - DCONJG( D( N ) )*X( N, J )
220 DO 150 I = 2, N - 1
221 B( I, J ) = B( I, J ) - DCONJG( DU( I-1 ) )*
222 $ X( I-1, J ) - DCONJG( D( I ) )*
223 $ X( I, J ) - DCONJG( DL( I ) )*
224 $ X( I+1, J )
225 150 CONTINUE
226 END IF
227 160 CONTINUE
228 END IF
229 END IF
230 RETURN
231 *
232 * End of ZLAGTM
233 *
234 END