1: *> \brief \b DLARZB applies a block reflector or its 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 DLARZB + dependencies
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11: *> [TGZ]</a>
12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlarzb.f">
13: *> [ZIP]</a>
14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlarzb.f">
15: *> [TXT]</a>
16: *> \endhtmlonly
17: *
18: * Definition:
19: * ===========
20: *
21: * SUBROUTINE DLARZB( 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: * DOUBLE PRECISION C( LDC, * ), T( LDT, * ), V( LDV, * ),
30: * $ WORK( LDWORK, * )
31: * ..
32: *
33: *
34: *> \par Purpose:
35: * =============
36: *>
37: *> \verbatim
38: *>
39: *> DLARZB applies a real block reflector H or its transpose H**T to
40: *> a real 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**T from the Left
52: *> = 'R': apply H or H**T 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**T (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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION array, dimension (LDC,N)
136: *> On entry, the M-by-N matrix C.
137: *> On exit, C is overwritten by H*C or H**T*C or C*H or C*H**T.
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 DOUBLE PRECISION 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 doubleOTHERcomputational
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 DLARZB( 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: DOUBLE PRECISION C( LDC, * ), T( LDT, * ), V( LDV, * ),
197: $ WORK( LDWORK, * )
198: * ..
199: *
200: * =====================================================================
201: *
202: * .. Parameters ..
203: DOUBLE PRECISION ONE
204: PARAMETER ( ONE = 1.0D+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 DCOPY, DGEMM, DTRMM, XERBLA
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( 'DLARZB', -INFO )
234: RETURN
235: END IF
236: *
237: IF( LSAME( TRANS, 'N' ) ) THEN
238: TRANST = 'T'
239: ELSE
240: TRANST = 'N'
241: END IF
242: *
243: IF( LSAME( SIDE, 'L' ) ) THEN
244: *
245: * Form H * C or H**T * C
246: *
247: * W( 1:n, 1:k ) = C( 1:k, 1:n )**T
248: *
249: DO 10 J = 1, K
250: CALL DCOPY( 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 )**T * V( 1:k, 1:l )**T
255: *
256: IF( L.GT.0 )
257: $ CALL DGEMM( 'Transpose', 'Transpose', N, K, L, ONE,
258: $ C( M-L+1, 1 ), LDC, V, LDV, ONE, WORK, LDWORK )
259: *
260: * W( 1:n, 1:k ) = W( 1:n, 1:k ) * T**T or W( 1:m, 1:k ) * T
261: *
262: CALL DTRMM( 'Right', 'Lower', TRANST, 'Non-unit', N, K, ONE, T,
263: $ LDT, WORK, LDWORK )
264: *
265: * C( 1:k, 1:n ) = C( 1:k, 1:n ) - W( 1:n, 1:k )**T
266: *
267: DO 30 J = 1, N
268: DO 20 I = 1, K
269: C( I, J ) = C( I, J ) - WORK( J, I )
270: 20 CONTINUE
271: 30 CONTINUE
272: *
273: * C( m-l+1:m, 1:n ) = C( m-l+1:m, 1:n ) - ...
274: * V( 1:k, 1:l )**T * W( 1:n, 1:k )**T
275: *
276: IF( L.GT.0 )
277: $ CALL DGEMM( 'Transpose', 'Transpose', L, N, K, -ONE, V, LDV,
278: $ WORK, LDWORK, ONE, C( M-L+1, 1 ), LDC )
279: *
280: ELSE IF( LSAME( SIDE, 'R' ) ) THEN
281: *
282: * Form C * H or C * H**T
283: *
284: * W( 1:m, 1:k ) = C( 1:m, 1:k )
285: *
286: DO 40 J = 1, K
287: CALL DCOPY( M, C( 1, J ), 1, WORK( 1, J ), 1 )
288: 40 CONTINUE
289: *
290: * W( 1:m, 1:k ) = W( 1:m, 1:k ) + ...
291: * C( 1:m, n-l+1:n ) * V( 1:k, 1:l )**T
292: *
293: IF( L.GT.0 )
294: $ CALL DGEMM( 'No transpose', 'Transpose', M, K, L, ONE,
295: $ C( 1, N-L+1 ), LDC, V, LDV, ONE, WORK, LDWORK )
296: *
297: * W( 1:m, 1:k ) = W( 1:m, 1:k ) * T or W( 1:m, 1:k ) * T**T
298: *
299: CALL DTRMM( 'Right', 'Lower', TRANS, 'Non-unit', M, K, ONE, T,
300: $ LDT, WORK, LDWORK )
301: *
302: * C( 1:m, 1:k ) = C( 1:m, 1:k ) - W( 1:m, 1:k )
303: *
304: DO 60 J = 1, K
305: DO 50 I = 1, M
306: C( I, J ) = C( I, J ) - WORK( I, J )
307: 50 CONTINUE
308: 60 CONTINUE
309: *
310: * C( 1:m, n-l+1:n ) = C( 1:m, n-l+1:n ) - ...
311: * W( 1:m, 1:k ) * V( 1:k, 1:l )
312: *
313: IF( L.GT.0 )
314: $ CALL DGEMM( 'No transpose', 'No transpose', M, L, K, -ONE,
315: $ WORK, LDWORK, V, LDV, ONE, C( 1, N-L+1 ), LDC )
316: *
317: END IF
318: *
319: RETURN
320: *
321: * End of DLARZB
322: *
323: END
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