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Mon Jan 27 09:28:39 2014 UTC (10 years, 3 months ago) by
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1: *> \brief \b ZLARZB applies a block reflector or its conjugate-transpose to a general matrix.
2: *
3: * =========== DOCUMENTATION ===========
4: *
5: * Online html documentation available at
6: * http://www.netlib.org/lapack/explore-html/
7: *
8: *> \htmlonly
9: *> Download ZLARZB + dependencies
10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zlarzb.f">
11: *> [TGZ]</a>
12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zlarzb.f">
13: *> [ZIP]</a>
14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zlarzb.f">
15: *> [TXT]</a>
16: *> \endhtmlonly
17: *
18: * Definition:
19: * ===========
20: *
21: * SUBROUTINE ZLARZB( SIDE, TRANS, DIRECT, STOREV, M, N, K, L, V,
22: * LDV, T, LDT, C, LDC, WORK, LDWORK )
23: *
24: * .. Scalar Arguments ..
25: * CHARACTER DIRECT, SIDE, STOREV, TRANS
26: * INTEGER K, L, LDC, LDT, LDV, LDWORK, M, N
27: * ..
28: * .. Array Arguments ..
29: * COMPLEX*16 C( LDC, * ), T( LDT, * ), V( LDV, * ),
30: * $ WORK( LDWORK, * )
31: * ..
32: *
33: *
34: *> \par Purpose:
35: * =============
36: *>
37: *> \verbatim
38: *>
39: *> ZLARZB applies a complex block reflector H or its transpose H**H
40: *> to a complex distributed M-by-N C from the left or the right.
41: *>
42: *> Currently, only STOREV = 'R' and DIRECT = 'B' are supported.
43: *> \endverbatim
44: *
45: * Arguments:
46: * ==========
47: *
48: *> \param[in] SIDE
49: *> \verbatim
50: *> SIDE is CHARACTER*1
51: *> = 'L': apply H or H**H from the Left
52: *> = 'R': apply H or H**H from the Right
53: *> \endverbatim
54: *>
55: *> \param[in] TRANS
56: *> \verbatim
57: *> TRANS is CHARACTER*1
58: *> = 'N': apply H (No transpose)
59: *> = 'C': apply H**H (Conjugate transpose)
60: *> \endverbatim
61: *>
62: *> \param[in] DIRECT
63: *> \verbatim
64: *> DIRECT is CHARACTER*1
65: *> Indicates how H is formed from a product of elementary
66: *> reflectors
67: *> = 'F': H = H(1) H(2) . . . H(k) (Forward, not supported yet)
68: *> = 'B': H = H(k) . . . H(2) H(1) (Backward)
69: *> \endverbatim
70: *>
71: *> \param[in] STOREV
72: *> \verbatim
73: *> STOREV is CHARACTER*1
74: *> Indicates how the vectors which define the elementary
75: *> reflectors are stored:
76: *> = 'C': Columnwise (not supported yet)
77: *> = 'R': Rowwise
78: *> \endverbatim
79: *>
80: *> \param[in] M
81: *> \verbatim
82: *> M is INTEGER
83: *> The number of rows of the matrix C.
84: *> \endverbatim
85: *>
86: *> \param[in] N
87: *> \verbatim
88: *> N is INTEGER
89: *> The number of columns of the matrix C.
90: *> \endverbatim
91: *>
92: *> \param[in] K
93: *> \verbatim
94: *> K is INTEGER
95: *> The order of the matrix T (= the number of elementary
96: *> reflectors whose product defines the block reflector).
97: *> \endverbatim
98: *>
99: *> \param[in] L
100: *> \verbatim
101: *> L is INTEGER
102: *> The number of columns of the matrix V containing the
103: *> meaningful part of the Householder reflectors.
104: *> If SIDE = 'L', M >= L >= 0, if SIDE = 'R', N >= L >= 0.
105: *> \endverbatim
106: *>
107: *> \param[in] V
108: *> \verbatim
109: *> V is COMPLEX*16 array, dimension (LDV,NV).
110: *> If STOREV = 'C', NV = K; if STOREV = 'R', NV = L.
111: *> \endverbatim
112: *>
113: *> \param[in] LDV
114: *> \verbatim
115: *> LDV is INTEGER
116: *> The leading dimension of the array V.
117: *> If STOREV = 'C', LDV >= L; if STOREV = 'R', LDV >= K.
118: *> \endverbatim
119: *>
120: *> \param[in] T
121: *> \verbatim
122: *> T is COMPLEX*16 array, dimension (LDT,K)
123: *> The triangular K-by-K matrix T in the representation of the
124: *> block reflector.
125: *> \endverbatim
126: *>
127: *> \param[in] LDT
128: *> \verbatim
129: *> LDT is INTEGER
130: *> The leading dimension of the array T. LDT >= K.
131: *> \endverbatim
132: *>
133: *> \param[in,out] C
134: *> \verbatim
135: *> C is COMPLEX*16 array, dimension (LDC,N)
136: *> On entry, the M-by-N matrix C.
137: *> On exit, C is overwritten by H*C or H**H*C or C*H or C*H**H.
138: *> \endverbatim
139: *>
140: *> \param[in] LDC
141: *> \verbatim
142: *> LDC is INTEGER
143: *> The leading dimension of the array C. LDC >= max(1,M).
144: *> \endverbatim
145: *>
146: *> \param[out] WORK
147: *> \verbatim
148: *> WORK is COMPLEX*16 array, dimension (LDWORK,K)
149: *> \endverbatim
150: *>
151: *> \param[in] LDWORK
152: *> \verbatim
153: *> LDWORK is INTEGER
154: *> The leading dimension of the array WORK.
155: *> If SIDE = 'L', LDWORK >= max(1,N);
156: *> if SIDE = 'R', LDWORK >= max(1,M).
157: *> \endverbatim
158: *
159: * Authors:
160: * ========
161: *
162: *> \author Univ. of Tennessee
163: *> \author Univ. of California Berkeley
164: *> \author Univ. of Colorado Denver
165: *> \author NAG Ltd.
166: *
167: *> \date September 2012
168: *
169: *> \ingroup complex16OTHERcomputational
170: *
171: *> \par Contributors:
172: * ==================
173: *>
174: *> A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA
175: *
176: *> \par Further Details:
177: * =====================
178: *>
179: *> \verbatim
180: *> \endverbatim
181: *>
182: * =====================================================================
183: SUBROUTINE ZLARZB( SIDE, TRANS, DIRECT, STOREV, M, N, K, L, V,
184: $ LDV, T, LDT, C, LDC, WORK, LDWORK )
185: *
186: * -- LAPACK computational routine (version 3.4.2) --
187: * -- LAPACK is a software package provided by Univ. of Tennessee, --
188: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
189: * September 2012
190: *
191: * .. Scalar Arguments ..
192: CHARACTER DIRECT, SIDE, STOREV, TRANS
193: INTEGER K, L, LDC, LDT, LDV, LDWORK, M, N
194: * ..
195: * .. Array Arguments ..
196: COMPLEX*16 C( LDC, * ), T( LDT, * ), V( LDV, * ),
197: $ WORK( LDWORK, * )
198: * ..
199: *
200: * =====================================================================
201: *
202: * .. Parameters ..
203: COMPLEX*16 ONE
204: PARAMETER ( ONE = ( 1.0D+0, 0.0D+0 ) )
205: * ..
206: * .. Local Scalars ..
207: CHARACTER TRANST
208: INTEGER I, INFO, J
209: * ..
210: * .. External Functions ..
211: LOGICAL LSAME
212: EXTERNAL LSAME
213: * ..
214: * .. External Subroutines ..
215: EXTERNAL XERBLA, ZCOPY, ZGEMM, ZLACGV, ZTRMM
216: * ..
217: * .. Executable Statements ..
218: *
219: * Quick return if possible
220: *
221: IF( M.LE.0 .OR. N.LE.0 )
222: $ RETURN
223: *
224: * Check for currently supported options
225: *
226: INFO = 0
227: IF( .NOT.LSAME( DIRECT, 'B' ) ) THEN
228: INFO = -3
229: ELSE IF( .NOT.LSAME( STOREV, 'R' ) ) THEN
230: INFO = -4
231: END IF
232: IF( INFO.NE.0 ) THEN
233: CALL XERBLA( 'ZLARZB', -INFO )
234: RETURN
235: END IF
236: *
237: IF( LSAME( TRANS, 'N' ) ) THEN
238: TRANST = 'C'
239: ELSE
240: TRANST = 'N'
241: END IF
242: *
243: IF( LSAME( SIDE, 'L' ) ) THEN
244: *
245: * Form H * C or H**H * C
246: *
247: * W( 1:n, 1:k ) = C( 1:k, 1:n )**H
248: *
249: DO 10 J = 1, K
250: CALL ZCOPY( N, C( J, 1 ), LDC, WORK( 1, J ), 1 )
251: 10 CONTINUE
252: *
253: * W( 1:n, 1:k ) = W( 1:n, 1:k ) + ...
254: * C( m-l+1:m, 1:n )**H * V( 1:k, 1:l )**T
255: *
256: IF( L.GT.0 )
257: $ CALL ZGEMM( 'Transpose', 'Conjugate transpose', N, K, L,
258: $ ONE, C( M-L+1, 1 ), LDC, V, LDV, ONE, WORK,
259: $ LDWORK )
260: *
261: * W( 1:n, 1:k ) = W( 1:n, 1:k ) * T**T or W( 1:m, 1:k ) * T
262: *
263: CALL ZTRMM( 'Right', 'Lower', TRANST, 'Non-unit', N, K, ONE, T,
264: $ LDT, WORK, LDWORK )
265: *
266: * C( 1:k, 1:n ) = C( 1:k, 1:n ) - W( 1:n, 1:k )**H
267: *
268: DO 30 J = 1, N
269: DO 20 I = 1, K
270: C( I, J ) = C( I, J ) - WORK( J, I )
271: 20 CONTINUE
272: 30 CONTINUE
273: *
274: * C( m-l+1:m, 1:n ) = C( m-l+1:m, 1:n ) - ...
275: * V( 1:k, 1:l )**H * W( 1:n, 1:k )**H
276: *
277: IF( L.GT.0 )
278: $ CALL ZGEMM( 'Transpose', 'Transpose', L, N, K, -ONE, V, LDV,
279: $ WORK, LDWORK, ONE, C( M-L+1, 1 ), LDC )
280: *
281: ELSE IF( LSAME( SIDE, 'R' ) ) THEN
282: *
283: * Form C * H or C * H**H
284: *
285: * W( 1:m, 1:k ) = C( 1:m, 1:k )
286: *
287: DO 40 J = 1, K
288: CALL ZCOPY( M, C( 1, J ), 1, WORK( 1, J ), 1 )
289: 40 CONTINUE
290: *
291: * W( 1:m, 1:k ) = W( 1:m, 1:k ) + ...
292: * C( 1:m, n-l+1:n ) * V( 1:k, 1:l )**H
293: *
294: IF( L.GT.0 )
295: $ CALL ZGEMM( 'No transpose', 'Transpose', M, K, L, ONE,
296: $ C( 1, N-L+1 ), LDC, V, LDV, ONE, WORK, LDWORK )
297: *
298: * W( 1:m, 1:k ) = W( 1:m, 1:k ) * conjg( T ) or
299: * W( 1:m, 1:k ) * T**H
300: *
301: DO 50 J = 1, K
302: CALL ZLACGV( K-J+1, T( J, J ), 1 )
303: 50 CONTINUE
304: CALL ZTRMM( 'Right', 'Lower', TRANS, 'Non-unit', M, K, ONE, T,
305: $ LDT, WORK, LDWORK )
306: DO 60 J = 1, K
307: CALL ZLACGV( K-J+1, T( J, J ), 1 )
308: 60 CONTINUE
309: *
310: * C( 1:m, 1:k ) = C( 1:m, 1:k ) - W( 1:m, 1:k )
311: *
312: DO 80 J = 1, K
313: DO 70 I = 1, M
314: C( I, J ) = C( I, J ) - WORK( I, J )
315: 70 CONTINUE
316: 80 CONTINUE
317: *
318: * C( 1:m, n-l+1:n ) = C( 1:m, n-l+1:n ) - ...
319: * W( 1:m, 1:k ) * conjg( V( 1:k, 1:l ) )
320: *
321: DO 90 J = 1, L
322: CALL ZLACGV( K, V( 1, J ), 1 )
323: 90 CONTINUE
324: IF( L.GT.0 )
325: $ CALL ZGEMM( 'No transpose', 'No transpose', M, L, K, -ONE,
326: $ WORK, LDWORK, V, LDV, ONE, C( 1, N-L+1 ), LDC )
327: DO 100 J = 1, L
328: CALL ZLACGV( K, V( 1, J ), 1 )
329: 100 CONTINUE
330: *
331: END IF
332: *
333: RETURN
334: *
335: * End of ZLARZB
336: *
337: END
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