1: *> \brief \b ZLAGTM 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.
2: *
3: * =========== DOCUMENTATION ===========
4: *
5: * Online html documentation available at
6: * http://www.netlib.org/lapack/explore-html/
7: *
8: *> \htmlonly
9: *> Download ZLAGTM + dependencies
10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zlagtm.f">
11: *> [TGZ]</a>
12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zlagtm.f">
13: *> [ZIP]</a>
14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zlagtm.f">
15: *> [TXT]</a>
16: *> \endhtmlonly
17: *
18: * Definition:
19: * ===========
20: *
21: * SUBROUTINE ZLAGTM( TRANS, N, NRHS, ALPHA, DL, D, DU, X, LDX, BETA,
22: * B, LDB )
23: *
24: * .. Scalar Arguments ..
25: * CHARACTER TRANS
26: * INTEGER LDB, LDX, N, NRHS
27: * DOUBLE PRECISION ALPHA, BETA
28: * ..
29: * .. Array Arguments ..
30: * COMPLEX*16 B( LDB, * ), D( * ), DL( * ), DU( * ),
31: * $ X( LDX, * )
32: * ..
33: *
34: *
35: *> \par Purpose:
36: * =============
37: *>
38: *> \verbatim
39: *>
40: *> ZLAGTM performs a matrix-vector product of the form
41: *>
42: *> B := alpha * A * X + beta * B
43: *>
44: *> where A is a tridiagonal matrix of order N, B and X are N by NRHS
45: *> matrices, and alpha and beta are real scalars, each of which may be
46: *> 0., 1., or -1.
47: *> \endverbatim
48: *
49: * Arguments:
50: * ==========
51: *
52: *> \param[in] TRANS
53: *> \verbatim
54: *> TRANS is CHARACTER*1
55: *> Specifies the operation applied to A.
56: *> = 'N': No transpose, B := alpha * A * X + beta * B
57: *> = 'T': Transpose, B := alpha * A**T * X + beta * B
58: *> = 'C': Conjugate transpose, B := alpha * A**H * X + beta * B
59: *> \endverbatim
60: *>
61: *> \param[in] N
62: *> \verbatim
63: *> N is INTEGER
64: *> The order of the matrix A. N >= 0.
65: *> \endverbatim
66: *>
67: *> \param[in] NRHS
68: *> \verbatim
69: *> NRHS is INTEGER
70: *> The number of right hand sides, i.e., the number of columns
71: *> of the matrices X and B.
72: *> \endverbatim
73: *>
74: *> \param[in] ALPHA
75: *> \verbatim
76: *> ALPHA is DOUBLE PRECISION
77: *> The scalar alpha. ALPHA must be 0., 1., or -1.; otherwise,
78: *> it is assumed to be 0.
79: *> \endverbatim
80: *>
81: *> \param[in] DL
82: *> \verbatim
83: *> DL is COMPLEX*16 array, dimension (N-1)
84: *> The (n-1) sub-diagonal elements of T.
85: *> \endverbatim
86: *>
87: *> \param[in] D
88: *> \verbatim
89: *> D is COMPLEX*16 array, dimension (N)
90: *> The diagonal elements of T.
91: *> \endverbatim
92: *>
93: *> \param[in] DU
94: *> \verbatim
95: *> DU is COMPLEX*16 array, dimension (N-1)
96: *> The (n-1) super-diagonal elements of T.
97: *> \endverbatim
98: *>
99: *> \param[in] X
100: *> \verbatim
101: *> X is COMPLEX*16 array, dimension (LDX,NRHS)
102: *> The N by NRHS matrix X.
103: *> \endverbatim
104: *>
105: *> \param[in] LDX
106: *> \verbatim
107: *> LDX is INTEGER
108: *> The leading dimension of the array X. LDX >= max(N,1).
109: *> \endverbatim
110: *>
111: *> \param[in] BETA
112: *> \verbatim
113: *> BETA is DOUBLE PRECISION
114: *> The scalar beta. BETA must be 0., 1., or -1.; otherwise,
115: *> it is assumed to be 1.
116: *> \endverbatim
117: *>
118: *> \param[in,out] B
119: *> \verbatim
120: *> B is COMPLEX*16 array, dimension (LDB,NRHS)
121: *> On entry, the N by NRHS matrix B.
122: *> On exit, B is overwritten by the matrix expression
123: *> B := alpha * A * X + beta * B.
124: *> \endverbatim
125: *>
126: *> \param[in] LDB
127: *> \verbatim
128: *> LDB is INTEGER
129: *> The leading dimension of the array B. LDB >= max(N,1).
130: *> \endverbatim
131: *
132: * Authors:
133: * ========
134: *
135: *> \author Univ. of Tennessee
136: *> \author Univ. of California Berkeley
137: *> \author Univ. of Colorado Denver
138: *> \author NAG Ltd.
139: *
140: *> \date December 2016
141: *
142: *> \ingroup complex16OTHERauxiliary
143: *
144: * =====================================================================
145: SUBROUTINE ZLAGTM( TRANS, N, NRHS, ALPHA, DL, D, DU, X, LDX, BETA,
146: $ B, LDB )
147: *
148: * -- LAPACK auxiliary routine (version 3.7.0) --
149: * -- LAPACK is a software package provided by Univ. of Tennessee, --
150: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
151: * December 2016
152: *
153: * .. Scalar Arguments ..
154: CHARACTER TRANS
155: INTEGER LDB, LDX, N, NRHS
156: DOUBLE PRECISION ALPHA, BETA
157: * ..
158: * .. Array Arguments ..
159: COMPLEX*16 B( LDB, * ), D( * ), DL( * ), DU( * ),
160: $ X( LDX, * )
161: * ..
162: *
163: * =====================================================================
164: *
165: * .. Parameters ..
166: DOUBLE PRECISION ONE, ZERO
167: PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
168: * ..
169: * .. Local Scalars ..
170: INTEGER I, J
171: * ..
172: * .. External Functions ..
173: LOGICAL LSAME
174: EXTERNAL LSAME
175: * ..
176: * .. Intrinsic Functions ..
177: INTRINSIC DCONJG
178: * ..
179: * .. Executable Statements ..
180: *
181: IF( N.EQ.0 )
182: $ RETURN
183: *
184: * Multiply B by BETA if BETA.NE.1.
185: *
186: IF( BETA.EQ.ZERO ) THEN
187: DO 20 J = 1, NRHS
188: DO 10 I = 1, N
189: B( I, J ) = ZERO
190: 10 CONTINUE
191: 20 CONTINUE
192: ELSE IF( BETA.EQ.-ONE ) THEN
193: DO 40 J = 1, NRHS
194: DO 30 I = 1, N
195: B( I, J ) = -B( I, J )
196: 30 CONTINUE
197: 40 CONTINUE
198: END IF
199: *
200: IF( ALPHA.EQ.ONE ) THEN
201: IF( LSAME( TRANS, 'N' ) ) THEN
202: *
203: * Compute B := B + A*X
204: *
205: DO 60 J = 1, NRHS
206: IF( N.EQ.1 ) THEN
207: B( 1, J ) = B( 1, J ) + D( 1 )*X( 1, J )
208: ELSE
209: B( 1, J ) = B( 1, J ) + D( 1 )*X( 1, J ) +
210: $ DU( 1 )*X( 2, J )
211: B( N, J ) = B( N, J ) + DL( N-1 )*X( N-1, J ) +
212: $ D( N )*X( N, J )
213: DO 50 I = 2, N - 1
214: B( I, J ) = B( I, J ) + DL( I-1 )*X( I-1, J ) +
215: $ D( I )*X( I, J ) + DU( I )*X( I+1, J )
216: 50 CONTINUE
217: END IF
218: 60 CONTINUE
219: ELSE IF( LSAME( TRANS, 'T' ) ) THEN
220: *
221: * Compute B := B + A**T * X
222: *
223: DO 80 J = 1, NRHS
224: IF( N.EQ.1 ) THEN
225: B( 1, J ) = B( 1, J ) + D( 1 )*X( 1, J )
226: ELSE
227: B( 1, J ) = B( 1, J ) + D( 1 )*X( 1, J ) +
228: $ DL( 1 )*X( 2, J )
229: B( N, J ) = B( N, J ) + DU( N-1 )*X( N-1, J ) +
230: $ D( N )*X( N, J )
231: DO 70 I = 2, N - 1
232: B( I, J ) = B( I, J ) + DU( I-1 )*X( I-1, J ) +
233: $ D( I )*X( I, J ) + DL( I )*X( I+1, J )
234: 70 CONTINUE
235: END IF
236: 80 CONTINUE
237: ELSE IF( LSAME( TRANS, 'C' ) ) THEN
238: *
239: * Compute B := B + A**H * X
240: *
241: DO 100 J = 1, NRHS
242: IF( N.EQ.1 ) THEN
243: B( 1, J ) = B( 1, J ) + DCONJG( D( 1 ) )*X( 1, J )
244: ELSE
245: B( 1, J ) = B( 1, J ) + DCONJG( D( 1 ) )*X( 1, J ) +
246: $ DCONJG( DL( 1 ) )*X( 2, J )
247: B( N, J ) = B( N, J ) + DCONJG( DU( N-1 ) )*
248: $ X( N-1, J ) + DCONJG( D( N ) )*X( N, J )
249: DO 90 I = 2, N - 1
250: B( I, J ) = B( I, J ) + DCONJG( DU( I-1 ) )*
251: $ X( I-1, J ) + DCONJG( D( I ) )*
252: $ X( I, J ) + DCONJG( DL( I ) )*
253: $ X( I+1, J )
254: 90 CONTINUE
255: END IF
256: 100 CONTINUE
257: END IF
258: ELSE IF( ALPHA.EQ.-ONE ) THEN
259: IF( LSAME( TRANS, 'N' ) ) THEN
260: *
261: * Compute B := B - A*X
262: *
263: DO 120 J = 1, NRHS
264: IF( N.EQ.1 ) THEN
265: B( 1, J ) = B( 1, J ) - D( 1 )*X( 1, J )
266: ELSE
267: B( 1, J ) = B( 1, J ) - D( 1 )*X( 1, J ) -
268: $ DU( 1 )*X( 2, J )
269: B( N, J ) = B( N, J ) - DL( N-1 )*X( N-1, J ) -
270: $ D( N )*X( N, J )
271: DO 110 I = 2, N - 1
272: B( I, J ) = B( I, J ) - DL( I-1 )*X( I-1, J ) -
273: $ D( I )*X( I, J ) - DU( I )*X( I+1, J )
274: 110 CONTINUE
275: END IF
276: 120 CONTINUE
277: ELSE IF( LSAME( TRANS, 'T' ) ) THEN
278: *
279: * Compute B := B - A**T *X
280: *
281: DO 140 J = 1, NRHS
282: IF( N.EQ.1 ) THEN
283: B( 1, J ) = B( 1, J ) - D( 1 )*X( 1, J )
284: ELSE
285: B( 1, J ) = B( 1, J ) - D( 1 )*X( 1, J ) -
286: $ DL( 1 )*X( 2, J )
287: B( N, J ) = B( N, J ) - DU( N-1 )*X( N-1, J ) -
288: $ D( N )*X( N, J )
289: DO 130 I = 2, N - 1
290: B( I, J ) = B( I, J ) - DU( I-1 )*X( I-1, J ) -
291: $ D( I )*X( I, J ) - DL( I )*X( I+1, J )
292: 130 CONTINUE
293: END IF
294: 140 CONTINUE
295: ELSE IF( LSAME( TRANS, 'C' ) ) THEN
296: *
297: * Compute B := B - A**H *X
298: *
299: DO 160 J = 1, NRHS
300: IF( N.EQ.1 ) THEN
301: B( 1, J ) = B( 1, J ) - DCONJG( D( 1 ) )*X( 1, J )
302: ELSE
303: B( 1, J ) = B( 1, J ) - DCONJG( D( 1 ) )*X( 1, J ) -
304: $ DCONJG( DL( 1 ) )*X( 2, J )
305: B( N, J ) = B( N, J ) - DCONJG( DU( N-1 ) )*
306: $ X( N-1, J ) - DCONJG( D( N ) )*X( N, J )
307: DO 150 I = 2, N - 1
308: B( I, J ) = B( I, J ) - DCONJG( DU( I-1 ) )*
309: $ X( I-1, J ) - DCONJG( D( I ) )*
310: $ X( I, J ) - DCONJG( DL( I ) )*
311: $ X( I+1, J )
312: 150 CONTINUE
313: END IF
314: 160 CONTINUE
315: END IF
316: END IF
317: RETURN
318: *
319: * End of ZLAGTM
320: *
321: END
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