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

 subroutine clarz ( character side, integer m, integer n, integer l, complex, dimension( * ) v, integer incv, complex tau, complex, dimension( ldc, * ) c, integer ldc, complex, dimension( * ) work )

CLARZ applies an elementary reflector (as returned by stzrzf) to a general matrix.

Purpose:
``` CLARZ applies a complex elementary reflector H to a complex
M-by-N matrix C, from either the left or the right. H is represented
in the form

H = I - tau * v * v**H

where tau is a complex scalar and v is a complex vector.

If tau = 0, then H is taken to be the unit matrix.

To apply H**H (the conjugate transpose of H), supply conjg(tau) instead
tau.

H is a product of k elementary reflectors as returned by CTZRZF.```
Parameters
 [in] SIDE ``` SIDE is CHARACTER*1 = 'L': form H * C = 'R': form C * H``` [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] L ``` L is INTEGER The number of entries of the vector V containing the meaningful part of the Householder vectors. If SIDE = 'L', M >= L >= 0, if SIDE = 'R', N >= L >= 0.``` [in] V ``` V is COMPLEX array, dimension (1+(L-1)*abs(INCV)) The vector v in the representation of H as returned by CTZRZF. V is not used if TAU = 0.``` [in] INCV ``` INCV is INTEGER The increment between elements of v. INCV <> 0.``` [in] TAU ``` TAU is COMPLEX The value tau in the representation of H.``` [in,out] C ``` C is COMPLEX array, dimension (LDC,N) On entry, the M-by-N matrix C. On exit, C is overwritten by the matrix H * C if SIDE = 'L', or C * H if SIDE = 'R'.``` [in] LDC ``` LDC is INTEGER The leading dimension of the array C. LDC >= max(1,M).``` [out] WORK ``` WORK is COMPLEX array, dimension (N) if SIDE = 'L' or (M) if SIDE = 'R'```
Contributors:
A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA
Further Details:
` `

Definition at line 146 of file clarz.f.

147*
148* -- LAPACK computational routine --
149* -- LAPACK is a software package provided by Univ. of Tennessee, --
150* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
151*
152* .. Scalar Arguments ..
153 CHARACTER SIDE
154 INTEGER INCV, L, LDC, M, N
155 COMPLEX TAU
156* ..
157* .. Array Arguments ..
158 COMPLEX C( LDC, * ), V( * ), WORK( * )
159* ..
160*
161* =====================================================================
162*
163* .. Parameters ..
164 COMPLEX ONE, ZERO
165 parameter( one = ( 1.0e+0, 0.0e+0 ),
166 \$ zero = ( 0.0e+0, 0.0e+0 ) )
167* ..
168* .. External Subroutines ..
169 EXTERNAL caxpy, ccopy, cgemv, cgerc, cgeru, clacgv
170* ..
171* .. External Functions ..
172 LOGICAL LSAME
173 EXTERNAL lsame
174* ..
175* .. Executable Statements ..
176*
177 IF( lsame( side, 'L' ) ) THEN
178*
179* Form H * C
180*
181 IF( tau.NE.zero ) THEN
182*
183* w( 1:n ) = conjg( C( 1, 1:n ) )
184*
185 CALL ccopy( n, c, ldc, work, 1 )
186 CALL clacgv( n, work, 1 )
187*
188* w( 1:n ) = conjg( w( 1:n ) + C( m-l+1:m, 1:n )**H * v( 1:l ) )
189*
190 CALL cgemv( 'Conjugate transpose', l, n, one, c( m-l+1, 1 ),
191 \$ ldc, v, incv, one, work, 1 )
192 CALL clacgv( n, work, 1 )
193*
194* C( 1, 1:n ) = C( 1, 1:n ) - tau * w( 1:n )
195*
196 CALL caxpy( n, -tau, work, 1, c, ldc )
197*
198* C( m-l+1:m, 1:n ) = C( m-l+1:m, 1:n ) - ...
199* tau * v( 1:l ) * w( 1:n )**H
200*
201 CALL cgeru( l, n, -tau, v, incv, work, 1, c( m-l+1, 1 ),
202 \$ ldc )
203 END IF
204*
205 ELSE
206*
207* Form C * H
208*
209 IF( tau.NE.zero ) THEN
210*
211* w( 1:m ) = C( 1:m, 1 )
212*
213 CALL ccopy( m, c, 1, work, 1 )
214*
215* w( 1:m ) = w( 1:m ) + C( 1:m, n-l+1:n, 1:n ) * v( 1:l )
216*
217 CALL cgemv( 'No transpose', m, l, one, c( 1, n-l+1 ), ldc,
218 \$ v, incv, one, work, 1 )
219*
220* C( 1:m, 1 ) = C( 1:m, 1 ) - tau * w( 1:m )
221*
222 CALL caxpy( m, -tau, work, 1, c, 1 )
223*
224* C( 1:m, n-l+1:n ) = C( 1:m, n-l+1:n ) - ...
225* tau * w( 1:m ) * v( 1:l )**H
226*
227 CALL cgerc( m, l, -tau, work, 1, v, incv, c( 1, n-l+1 ),
228 \$ ldc )
229*
230 END IF
231*
232 END IF
233*
234 RETURN
235*
236* End of CLARZ
237*
subroutine caxpy(n, ca, cx, incx, cy, incy)
CAXPY
Definition caxpy.f:88
subroutine ccopy(n, cx, incx, cy, incy)
CCOPY
Definition ccopy.f:81
subroutine cgemv(trans, m, n, alpha, a, lda, x, incx, beta, y, incy)
CGEMV
Definition cgemv.f:160
subroutine cgerc(m, n, alpha, x, incx, y, incy, a, lda)
CGERC
Definition cgerc.f:130
subroutine cgeru(m, n, alpha, x, incx, y, incy, a, lda)
CGERU
Definition cgeru.f:130
subroutine clacgv(n, x, incx)
CLACGV conjugates a complex vector.
Definition clacgv.f:74
logical function lsame(ca, cb)
LSAME
Definition lsame.f:48
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