LAPACK 3.12.0 LAPACK: Linear Algebra PACKage
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## ◆ clarzb()

 subroutine clarzb ( character side, character trans, character direct, character storev, integer m, integer n, integer k, integer l, complex, dimension( ldv, * ) v, integer ldv, complex, dimension( ldt, * ) t, integer ldt, complex, dimension( ldc, * ) c, integer ldc, complex, dimension( ldwork, * ) work, integer ldwork )

CLARZB applies a block reflector or its conjugate-transpose to a general matrix.

Purpose:
``` CLARZB applies a complex block reflector H or its transpose H**H
to a complex distributed M-by-N  C from the left or the right.

Currently, only STOREV = 'R' and DIRECT = 'B' are supported.```
Parameters
 [in] SIDE ``` SIDE is CHARACTER*1 = 'L': apply H or H**H from the Left = 'R': apply H or H**H from the Right``` [in] TRANS ``` TRANS is CHARACTER*1 = 'N': apply H (No transpose) = 'C': apply H**H (Conjugate transpose)``` [in] DIRECT ``` DIRECT is CHARACTER*1 Indicates how H is formed from a product of elementary reflectors = 'F': H = H(1) H(2) . . . H(k) (Forward, not supported yet) = 'B': H = H(k) . . . H(2) H(1) (Backward)``` [in] STOREV ``` STOREV is CHARACTER*1 Indicates how the vectors which define the elementary reflectors are stored: = 'C': Columnwise (not supported yet) = 'R': Rowwise``` [in] M ``` M is INTEGER The number of rows of the matrix C.``` [in] N ``` N is INTEGER The number of columns of the matrix C.``` [in] K ``` K is INTEGER The order of the matrix T (= the number of elementary reflectors whose product defines the block reflector).``` [in] L ``` L is INTEGER The number of columns of the matrix V containing the meaningful part of the Householder reflectors. If SIDE = 'L', M >= L >= 0, if SIDE = 'R', N >= L >= 0.``` [in] V ``` V is COMPLEX array, dimension (LDV,NV). If STOREV = 'C', NV = K; if STOREV = 'R', NV = L.``` [in] LDV ``` LDV is INTEGER The leading dimension of the array V. If STOREV = 'C', LDV >= L; if STOREV = 'R', LDV >= K.``` [in] T ``` T is COMPLEX array, dimension (LDT,K) The triangular K-by-K matrix T in the representation of the block reflector.``` [in] LDT ``` LDT is INTEGER The leading dimension of the array T. LDT >= K.``` [in,out] C ``` C is COMPLEX array, dimension (LDC,N) On entry, the M-by-N matrix C. On exit, C is overwritten by H*C or H**H*C or C*H or C*H**H.``` [in] LDC ``` LDC is INTEGER The leading dimension of the array C. LDC >= max(1,M).``` [out] WORK ` WORK is COMPLEX array, dimension (LDWORK,K)` [in] LDWORK ``` LDWORK is INTEGER The leading dimension of the array WORK. If SIDE = 'L', LDWORK >= max(1,N); if SIDE = 'R', LDWORK >= max(1,M).```
Contributors:
A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA
Further Details:
` `

Definition at line 181 of file clarzb.f.

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 COMPLEX C( LDC, * ), T( LDT, * ), V( LDV, * ),
194 \$ WORK( LDWORK, * )
195* ..
196*
197* =====================================================================
198*
199* .. Parameters ..
200 COMPLEX ONE
201 parameter( one = ( 1.0e+0, 0.0e+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 ccopy, cgemm, clacgv, ctrmm, 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( 'CLARZB', -info )
231 RETURN
232 END IF
233*
234 IF( lsame( trans, 'N' ) ) THEN
235 transt = 'C'
236 ELSE
237 transt = 'N'
238 END IF
239*
240 IF( lsame( side, 'L' ) ) THEN
241*
242* Form H * C or H**H * C
243*
244* W( 1:n, 1:k ) = C( 1:k, 1:n )**H
245*
246 DO 10 j = 1, k
247 CALL ccopy( 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 )**H * V( 1:k, 1:l )**T
252*
253 IF( l.GT.0 )
254 \$ CALL cgemm( 'Transpose', 'Conjugate transpose', n, k, l,
255 \$ one, c( m-l+1, 1 ), ldc, v, ldv, one, work,
256 \$ ldwork )
257*
258* W( 1:n, 1:k ) = W( 1:n, 1:k ) * T**T or W( 1:m, 1:k ) * T
259*
260 CALL ctrmm( 'Right', 'Lower', transt, 'Non-unit', n, k, one, t,
261 \$ ldt, work, ldwork )
262*
263* C( 1:k, 1:n ) = C( 1:k, 1:n ) - W( 1:n, 1:k )**H
264*
265 DO 30 j = 1, n
266 DO 20 i = 1, k
267 c( i, j ) = c( i, j ) - work( j, i )
268 20 CONTINUE
269 30 CONTINUE
270*
271* C( m-l+1:m, 1:n ) = C( m-l+1:m, 1:n ) - ...
272* V( 1:k, 1:l )**H * W( 1:n, 1:k )**H
273*
274 IF( l.GT.0 )
275 \$ CALL cgemm( 'Transpose', 'Transpose', l, n, k, -one, v, ldv,
276 \$ work, ldwork, one, c( m-l+1, 1 ), ldc )
277*
278 ELSE IF( lsame( side, 'R' ) ) THEN
279*
280* Form C * H or C * H**H
281*
282* W( 1:m, 1:k ) = C( 1:m, 1:k )
283*
284 DO 40 j = 1, k
285 CALL ccopy( m, c( 1, j ), 1, work( 1, j ), 1 )
286 40 CONTINUE
287*
288* W( 1:m, 1:k ) = W( 1:m, 1:k ) + ...
289* C( 1:m, n-l+1:n ) * V( 1:k, 1:l )**H
290*
291 IF( l.GT.0 )
292 \$ CALL cgemm( 'No transpose', 'Transpose', m, k, l, one,
293 \$ c( 1, n-l+1 ), ldc, v, ldv, one, work, ldwork )
294*
295* W( 1:m, 1:k ) = W( 1:m, 1:k ) * conjg( T ) or
296* W( 1:m, 1:k ) * T**H
297*
298 DO 50 j = 1, k
299 CALL clacgv( k-j+1, t( j, j ), 1 )
300 50 CONTINUE
301 CALL ctrmm( 'Right', 'Lower', trans, 'Non-unit', m, k, one, t,
302 \$ ldt, work, ldwork )
303 DO 60 j = 1, k
304 CALL clacgv( k-j+1, t( j, j ), 1 )
305 60 CONTINUE
306*
307* C( 1:m, 1:k ) = C( 1:m, 1:k ) - W( 1:m, 1:k )
308*
309 DO 80 j = 1, k
310 DO 70 i = 1, m
311 c( i, j ) = c( i, j ) - work( i, j )
312 70 CONTINUE
313 80 CONTINUE
314*
315* C( 1:m, n-l+1:n ) = C( 1:m, n-l+1:n ) - ...
316* W( 1:m, 1:k ) * conjg( V( 1:k, 1:l ) )
317*
318 DO 90 j = 1, l
319 CALL clacgv( k, v( 1, j ), 1 )
320 90 CONTINUE
321 IF( l.GT.0 )
322 \$ CALL cgemm( 'No transpose', 'No transpose', m, l, k, -one,
323 \$ work, ldwork, v, ldv, one, c( 1, n-l+1 ), ldc )
324 DO 100 j = 1, l
325 CALL clacgv( k, v( 1, j ), 1 )
326 100 CONTINUE
327*
328 END IF
329*
330 RETURN
331*
332* End of CLARZB
333*
subroutine xerbla(srname, info)
Definition cblat2.f:3285
subroutine ccopy(n, cx, incx, cy, incy)
CCOPY
Definition ccopy.f:81
subroutine cgemm(transa, transb, m, n, k, alpha, a, lda, b, ldb, beta, c, ldc)
CGEMM
Definition cgemm.f:188
subroutine clacgv(n, x, incx)
CLACGV conjugates a complex vector.
Definition clacgv.f:74
logical function lsame(ca, cb)
LSAME
Definition lsame.f:48
subroutine ctrmm(side, uplo, transa, diag, m, n, alpha, a, lda, b, ldb)
CTRMM
Definition ctrmm.f:177
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