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1.1 bertrand 1: SUBROUTINE ZLAGTM( TRANS, N, NRHS, ALPHA, DL, D, DU, X, LDX, BETA,
2: $ B, LDB )
3: *
4: * -- LAPACK auxiliary routine (version 3.2) --
5: * -- LAPACK is a software package provided by Univ. of Tennessee, --
6: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
7: * November 2006
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'*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'*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