1 *> \brief \b CLARZB applies a block reflector or its conjugate-transpose to a general matrix.
3 * =========== DOCUMENTATION ===========
5 * Online html documentation available at
6 * http://www.netlib.org/lapack/explore-html/
9 *> Download CLARZB + dependencies
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21 * SUBROUTINE CLARZB( SIDE, TRANS, DIRECT, STOREV, M, N, K, L, V,
22 * LDV, T, LDT, C, LDC, WORK, LDWORK )
24 * .. Scalar Arguments ..
25 * CHARACTER DIRECT, SIDE, STOREV, TRANS
26 * INTEGER K, L, LDC, LDT, LDV, LDWORK, M, N
28 * .. Array Arguments ..
29 * COMPLEX C( LDC, * ), T( LDT, * ), V( LDV, * ),
39 *> CLARZB 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.
42 *> Currently, only STOREV = 'R' and DIRECT = 'B' are supported.
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
57 *> TRANS is CHARACTER*1
58 *> = 'N': apply H (No transpose)
59 *> = 'C': apply H**H (Conjugate transpose)
64 *> DIRECT is CHARACTER*1
65 *> Indicates how H is formed from a product of elementary
67 *> = 'F': H = H(1) H(2) . . . H(k) (Forward, not supported yet)
68 *> = 'B': H = H(k) . . . H(2) H(1) (Backward)
73 *> STOREV is CHARACTER*1
74 *> Indicates how the vectors which define the elementary
75 *> reflectors are stored:
76 *> = 'C': Columnwise (not supported yet)
83 *> The number of rows of the matrix C.
89 *> The number of columns of the matrix C.
95 *> The order of the matrix T (= the number of elementary
96 *> reflectors whose product defines the block reflector).
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.
109 *> V is COMPLEX array, dimension (LDV,NV).
110 *> If STOREV = 'C', NV = K; if STOREV = 'R', NV = L.
116 *> The leading dimension of the array V.
117 *> If STOREV = 'C', LDV >= L; if STOREV = 'R', LDV >= K.
122 *> T is COMPLEX array, dimension (LDT,K)
123 *> The triangular K-by-K matrix T in the representation of the
130 *> The leading dimension of the array T. LDT >= K.
135 *> C is COMPLEX 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.
143 *> The leading dimension of the array C. LDC >= max(1,M).
148 *> WORK is COMPLEX array, dimension (LDWORK,K)
154 *> The leading dimension of the array WORK.
155 *> If SIDE = 'L', LDWORK >= max(1,N);
156 *> if SIDE = 'R', LDWORK >= max(1,M).
162 *> \author Univ. of Tennessee
163 *> \author Univ. of California Berkeley
164 *> \author Univ. of Colorado Denver
167 *> \date September 2012
169 *> \ingroup complexOTHERcomputational
171 *> \par Contributors:
174 *> A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA
176 *> \par Further Details:
177 * =====================
182 * =====================================================================
183 SUBROUTINE CLARZB( SIDE, TRANS, DIRECT, STOREV, M, N, K, L, V,
184 $ LDV, T, LDT, C, LDC, WORK, LDWORK )
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..--
191 * .. Scalar Arguments ..
192 CHARACTER DIRECT, SIDE, STOREV, TRANS
193 INTEGER K, L, LDC, LDT, LDV, LDWORK, M, N
195 * .. Array Arguments ..
196 COMPLEX C( LDC, * ), T( LDT, * ), V( LDV, * ),
200 * =====================================================================
204 PARAMETER ( ONE = ( 1.0E+0, 0.0E+0 ) )
206 * .. Local Scalars ..
210 * .. External Functions ..
214 * .. External Subroutines ..
215 EXTERNAL CCOPY, CGEMM, CLACGV, CTRMM, XERBLA
217 * .. Executable Statements ..
219 * Quick return if possible
221 IF( M.LE.0 .OR. N.LE.0 )
224 * Check for currently supported options
227 IF( .NOT.LSAME( DIRECT, 'B' ) ) THEN
229 ELSE IF( .NOT.LSAME( STOREV, 'R' ) ) THEN
233 CALL XERBLA( 'CLARZB', -INFO )
237 IF( LSAME( TRANS, 'N' ) ) THEN
243 IF( LSAME( SIDE, 'L' ) ) THEN
245 * Form H * C or H**H * C
247 * W( 1:n, 1:k ) = C( 1:k, 1:n )**H
250 CALL CCOPY( N, C( J, 1 ), LDC, WORK( 1, J ), 1 )
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
257 $ CALL CGEMM( 'Transpose', 'Conjugate transpose', N, K, L,
258 $ ONE, C( M-L+1, 1 ), LDC, V, LDV, ONE, WORK,
261 * W( 1:n, 1:k ) = W( 1:n, 1:k ) * T**T or W( 1:m, 1:k ) * T
263 CALL CTRMM( 'Right', 'Lower', TRANST, 'Non-unit', N, K, ONE, T,
264 $ LDT, WORK, LDWORK )
266 * C( 1:k, 1:n ) = C( 1:k, 1:n ) - W( 1:n, 1:k )**H
270 C( I, J ) = C( I, J ) - WORK( J, I )
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
278 $ CALL CGEMM( 'Transpose', 'Transpose', L, N, K, -ONE, V, LDV,
279 $ WORK, LDWORK, ONE, C( M-L+1, 1 ), LDC )
281 ELSE IF( LSAME( SIDE, 'R' ) ) THEN
283 * Form C * H or C * H**H
285 * W( 1:m, 1:k ) = C( 1:m, 1:k )
288 CALL CCOPY( M, C( 1, J ), 1, WORK( 1, J ), 1 )
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
295 $ CALL CGEMM( 'No transpose', 'Transpose', M, K, L, ONE,
296 $ C( 1, N-L+1 ), LDC, V, LDV, ONE, WORK, LDWORK )
298 * W( 1:m, 1:k ) = W( 1:m, 1:k ) * conjg( T ) or
299 * W( 1:m, 1:k ) * T**H
302 CALL CLACGV( K-J+1, T( J, J ), 1 )
304 CALL CTRMM( 'Right', 'Lower', TRANS, 'Non-unit', M, K, ONE, T,
305 $ LDT, WORK, LDWORK )
307 CALL CLACGV( K-J+1, T( J, J ), 1 )
310 * C( 1:m, 1:k ) = C( 1:m, 1:k ) - W( 1:m, 1:k )
314 C( I, J ) = C( I, J ) - WORK( I, J )
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 ) )
322 CALL CLACGV( K, V( 1, J ), 1 )
325 $ CALL CGEMM( 'No transpose', 'No transpose', M, L, K, -ONE,
326 $ WORK, LDWORK, V, LDV, ONE, C( 1, N-L+1 ), LDC )
328 CALL CLACGV( K, V( 1, J ), 1 )