LAPACK  3.10.0
LAPACK: Linear Algebra PACKage
slarzb.f
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1 *> \brief \b SLARZB 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 SLARZB + dependencies
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11 *> [TGZ]</a>
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13 *> [ZIP]</a>
14 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/slarzb.f">
15 *> [TXT]</a>
16 *> \endhtmlonly
17 *
18 * Definition:
19 * ===========
20 *
21 * SUBROUTINE SLARZB( 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 * REAL C( LDC, * ), T( LDT, * ), V( LDV, * ),
30 * $ WORK( LDWORK, * )
31 * ..
32 *
33 *
34 *> \par Purpose:
35 * =============
36 *>
37 *> \verbatim
38 *>
39 *> SLARZB 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 REAL 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 REAL 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 REAL 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 REAL 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 *> \ingroup realOTHERcomputational
168 *
169 *> \par Contributors:
170 * ==================
171 *>
172 *> A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA
173 *
174 *> \par Further Details:
175 * =====================
176 *>
177 *> \verbatim
178 *> \endverbatim
179 *>
180 * =====================================================================
181  SUBROUTINE slarzb( SIDE, TRANS, DIRECT, STOREV, M, N, K, L, V,
182  $ LDV, T, LDT, C, LDC, WORK, LDWORK )
183 *
184 * -- LAPACK computational routine --
185 * -- LAPACK is a software package provided by Univ. of Tennessee, --
186 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
187 *
188 * .. Scalar Arguments ..
189  CHARACTER DIRECT, SIDE, STOREV, TRANS
190  INTEGER K, L, LDC, LDT, LDV, LDWORK, M, N
191 * ..
192 * .. Array Arguments ..
193  REAL C( LDC, * ), T( LDT, * ), V( LDV, * ),
194  $ work( ldwork, * )
195 * ..
196 *
197 * =====================================================================
198 *
199 * .. Parameters ..
200  REAL ONE
201  parameter( one = 1.0e+0 )
202 * ..
203 * .. Local Scalars ..
204  CHARACTER TRANST
205  INTEGER I, INFO, J
206 * ..
207 * .. External Functions ..
208  LOGICAL LSAME
209  EXTERNAL lsame
210 * ..
211 * .. External Subroutines ..
212  EXTERNAL scopy, sgemm, strmm, xerbla
213 * ..
214 * .. Executable Statements ..
215 *
216 * Quick return if possible
217 *
218  IF( m.LE.0 .OR. n.LE.0 )
219  $ RETURN
220 *
221 * Check for currently supported options
222 *
223  info = 0
224  IF( .NOT.lsame( direct, 'B' ) ) THEN
225  info = -3
226  ELSE IF( .NOT.lsame( storev, 'R' ) ) THEN
227  info = -4
228  END IF
229  IF( info.NE.0 ) THEN
230  CALL xerbla( 'SLARZB', -info )
231  RETURN
232  END IF
233 *
234  IF( lsame( trans, 'N' ) ) THEN
235  transt = 'T'
236  ELSE
237  transt = 'N'
238  END IF
239 *
240  IF( lsame( side, 'L' ) ) THEN
241 *
242 * Form H * C or H**T * C
243 *
244 * W( 1:n, 1:k ) = C( 1:k, 1:n )**T
245 *
246  DO 10 j = 1, k
247  CALL scopy( n, c( j, 1 ), ldc, work( 1, j ), 1 )
248  10 CONTINUE
249 *
250 * W( 1:n, 1:k ) = W( 1:n, 1:k ) + ...
251 * C( m-l+1:m, 1:n )**T * V( 1:k, 1:l )**T
252 *
253  IF( l.GT.0 )
254  $ CALL sgemm( 'Transpose', 'Transpose', n, k, l, one,
255  $ c( m-l+1, 1 ), ldc, v, ldv, one, work, ldwork )
256 *
257 * W( 1:n, 1:k ) = W( 1:n, 1:k ) * T**T or W( 1:m, 1:k ) * T
258 *
259  CALL strmm( 'Right', 'Lower', transt, 'Non-unit', n, k, one, t,
260  $ ldt, work, ldwork )
261 *
262 * C( 1:k, 1:n ) = C( 1:k, 1:n ) - W( 1:n, 1:k )**T
263 *
264  DO 30 j = 1, n
265  DO 20 i = 1, k
266  c( i, j ) = c( i, j ) - work( j, i )
267  20 CONTINUE
268  30 CONTINUE
269 *
270 * C( m-l+1:m, 1:n ) = C( m-l+1:m, 1:n ) - ...
271 * V( 1:k, 1:l )**T * W( 1:n, 1:k )**T
272 *
273  IF( l.GT.0 )
274  $ CALL sgemm( 'Transpose', 'Transpose', l, n, k, -one, v, ldv,
275  $ work, ldwork, one, c( m-l+1, 1 ), ldc )
276 *
277  ELSE IF( lsame( side, 'R' ) ) THEN
278 *
279 * Form C * H or C * H**T
280 *
281 * W( 1:m, 1:k ) = C( 1:m, 1:k )
282 *
283  DO 40 j = 1, k
284  CALL scopy( m, c( 1, j ), 1, work( 1, j ), 1 )
285  40 CONTINUE
286 *
287 * W( 1:m, 1:k ) = W( 1:m, 1:k ) + ...
288 * C( 1:m, n-l+1:n ) * V( 1:k, 1:l )**T
289 *
290  IF( l.GT.0 )
291  $ CALL sgemm( 'No transpose', 'Transpose', m, k, l, one,
292  $ c( 1, n-l+1 ), ldc, v, ldv, one, work, ldwork )
293 *
294 * W( 1:m, 1:k ) = W( 1:m, 1:k ) * T or W( 1:m, 1:k ) * T**T
295 *
296  CALL strmm( 'Right', 'Lower', trans, 'Non-unit', m, k, one, t,
297  $ ldt, work, ldwork )
298 *
299 * C( 1:m, 1:k ) = C( 1:m, 1:k ) - W( 1:m, 1:k )
300 *
301  DO 60 j = 1, k
302  DO 50 i = 1, m
303  c( i, j ) = c( i, j ) - work( i, j )
304  50 CONTINUE
305  60 CONTINUE
306 *
307 * C( 1:m, n-l+1:n ) = C( 1:m, n-l+1:n ) - ...
308 * W( 1:m, 1:k ) * V( 1:k, 1:l )
309 *
310  IF( l.GT.0 )
311  $ CALL sgemm( 'No transpose', 'No transpose', m, l, k, -one,
312  $ work, ldwork, v, ldv, one, c( 1, n-l+1 ), ldc )
313 *
314  END IF
315 *
316  RETURN
317 *
318 * End of SLARZB
319 *
320  END
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
subroutine slarzb(SIDE, TRANS, DIRECT, STOREV, M, N, K, L, V, LDV, T, LDT, C, LDC, WORK, LDWORK)
SLARZB applies a block reflector or its transpose to a general matrix.
Definition: slarzb.f:183
subroutine scopy(N, SX, INCX, SY, INCY)
SCOPY
Definition: scopy.f:82
subroutine strmm(SIDE, UPLO, TRANSA, DIAG, M, N, ALPHA, A, LDA, B, LDB)
STRMM
Definition: strmm.f:177
subroutine sgemm(TRANSA, TRANSB, M, N, K, ALPHA, A, LDA, B, LDB, BETA, C, LDC)
SGEMM
Definition: sgemm.f:187