LAPACK 3.12.0
LAPACK: Linear Algebra PACKage
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◆ zlarzb()

subroutine zlarzb ( character  side,
character  trans,
character  direct,
character  storev,
integer  m,
integer  n,
integer  k,
integer  l,
complex*16, dimension( ldv, * )  v,
integer  ldv,
complex*16, dimension( ldt, * )  t,
integer  ldt,
complex*16, dimension( ldc, * )  c,
integer  ldc,
complex*16, dimension( ldwork, * )  work,
integer  ldwork 
)

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

Download ZLARZB + dependencies [TGZ] [ZIP] [TXT]

Purpose:
 ZLARZB 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*16 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*16 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*16 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*16 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).
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Contributors:
A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA
Further Details:

Definition at line 181 of file zlarzb.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*16 C( LDC, * ), T( LDT, * ), V( LDV, * ),
194 $ WORK( LDWORK, * )
195* ..
196*
197* =====================================================================
198*
199* .. Parameters ..
200 COMPLEX*16 ONE
201 parameter( one = ( 1.0d+0, 0.0d+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 xerbla, zcopy, zgemm, zlacgv, ztrmm
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( 'ZLARZB', -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 zcopy( 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 zgemm( '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 ztrmm( '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 zgemm( '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 zcopy( 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 zgemm( '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 zlacgv( k-j+1, t( j, j ), 1 )
300 50 CONTINUE
301 CALL ztrmm( 'Right', 'Lower', trans, 'Non-unit', m, k, one, t,
302 $ ldt, work, ldwork )
303 DO 60 j = 1, k
304 CALL zlacgv( 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 zlacgv( k, v( 1, j ), 1 )
320 90 CONTINUE
321 IF( l.GT.0 )
322 $ CALL zgemm( '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 zlacgv( k, v( 1, j ), 1 )
326 100 CONTINUE
327*
328 END IF
329*
330 RETURN
331*
332* End of ZLARZB
333*
xerbla
subroutine xerbla(srname, info)
Definition cblat2.f:3285
zcopy
subroutine zcopy(n, zx, incx, zy, incy)
ZCOPY
Definition zcopy.f:81
zgemm
subroutine zgemm(transa, transb, m, n, k, alpha, a, lda, b, ldb, beta, c, ldc)
ZGEMM
Definition zgemm.f:188
zlacgv
subroutine zlacgv(n, x, incx)
ZLACGV conjugates a complex vector.
Definition zlacgv.f:74
lsame
logical function lsame(ca, cb)
LSAME
Definition lsame.f:48
ztrmm
subroutine ztrmm(side, uplo, transa, diag, m, n, alpha, a, lda, b, ldb)
ZTRMM
Definition ztrmm.f:177
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