LAPACK  3.8.0
LAPACK: Linear Algebra PACKage
dlarzb.f
Go to the documentation of this file.
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
10 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlarzb.f">
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 December 2016
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 3.7.0) --
187 * -- LAPACK is a software package provided by Univ. of Tennessee, --
188 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
189 * December 2016
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
subroutine dcopy(N, DX, INCX, DY, INCY)
DCOPY
Definition: dcopy.f:84
subroutine dtrmm(SIDE, UPLO, TRANSA, DIAG, M, N, ALPHA, A, LDA, B, LDB)
DTRMM
Definition: dtrmm.f:179
subroutine dgemm(TRANSA, TRANSB, M, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
DGEMM
Definition: dgemm.f:189
subroutine dlarzb(SIDE, TRANS, DIRECT, STOREV, M, N, K, L, V, LDV, T, LDT, C, LDC, WORK, LDWORK)
DLARZB applies a block reflector or its transpose to a general matrix.
Definition: dlarzb.f:185
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62