 LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
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## ◆ clarf()

 subroutine clarf ( character SIDE, integer M, integer N, complex, dimension( * ) V, integer INCV, complex TAU, complex, dimension( ldc, * ) C, integer LDC, complex, dimension( * ) WORK )

CLARF applies an elementary reflector to a general rectangular matrix.

Purpose:
``` CLARF 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.```
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] V ``` V is COMPLEX array, dimension (1 + (M-1)*abs(INCV)) if SIDE = 'L' or (1 + (N-1)*abs(INCV)) if SIDE = 'R' The vector v in the representation of H. 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'```

Definition at line 127 of file clarf.f.

128*
129* -- LAPACK auxiliary routine --
130* -- LAPACK is a software package provided by Univ. of Tennessee, --
131* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
132*
133* .. Scalar Arguments ..
134 CHARACTER SIDE
135 INTEGER INCV, LDC, M, N
136 COMPLEX TAU
137* ..
138* .. Array Arguments ..
139 COMPLEX C( LDC, * ), V( * ), WORK( * )
140* ..
141*
142* =====================================================================
143*
144* .. Parameters ..
145 COMPLEX ONE, ZERO
146 parameter( one = ( 1.0e+0, 0.0e+0 ),
147 \$ zero = ( 0.0e+0, 0.0e+0 ) )
148* ..
149* .. Local Scalars ..
150 LOGICAL APPLYLEFT
151 INTEGER I, LASTV, LASTC
152* ..
153* .. External Subroutines ..
154 EXTERNAL cgemv, cgerc
155* ..
156* .. External Functions ..
157 LOGICAL LSAME
158 INTEGER ILACLR, ILACLC
159 EXTERNAL lsame, ilaclr, ilaclc
160* ..
161* .. Executable Statements ..
162*
163 applyleft = lsame( side, 'L' )
164 lastv = 0
165 lastc = 0
166 IF( tau.NE.zero ) THEN
167! Set up variables for scanning V. LASTV begins pointing to the end
168! of V.
169 IF( applyleft ) THEN
170 lastv = m
171 ELSE
172 lastv = n
173 END IF
174 IF( incv.GT.0 ) THEN
175 i = 1 + (lastv-1) * incv
176 ELSE
177 i = 1
178 END IF
179! Look for the last non-zero row in V.
180 DO WHILE( lastv.GT.0 .AND. v( i ).EQ.zero )
181 lastv = lastv - 1
182 i = i - incv
183 END DO
184 IF( applyleft ) THEN
185! Scan for the last non-zero column in C(1:lastv,:).
186 lastc = ilaclc(lastv, n, c, ldc)
187 ELSE
188! Scan for the last non-zero row in C(:,1:lastv).
189 lastc = ilaclr(m, lastv, c, ldc)
190 END IF
191 END IF
192! Note that lastc.eq.0 renders the BLAS operations null; no special
193! case is needed at this level.
194 IF( applyleft ) THEN
195*
196* Form H * C
197*
198 IF( lastv.GT.0 ) THEN
199*
200* w(1:lastc,1) := C(1:lastv,1:lastc)**H * v(1:lastv,1)
201*
202 CALL cgemv( 'Conjugate transpose', lastv, lastc, one,
203 \$ c, ldc, v, incv, zero, work, 1 )
204*
205* C(1:lastv,1:lastc) := C(...) - v(1:lastv,1) * w(1:lastc,1)**H
206*
207 CALL cgerc( lastv, lastc, -tau, v, incv, work, 1, c, ldc )
208 END IF
209 ELSE
210*
211* Form C * H
212*
213 IF( lastv.GT.0 ) THEN
214*
215* w(1:lastc,1) := C(1:lastc,1:lastv) * v(1:lastv,1)
216*
217 CALL cgemv( 'No transpose', lastc, lastv, one, c, ldc,
218 \$ v, incv, zero, work, 1 )
219*
220* C(1:lastc,1:lastv) := C(...) - w(1:lastc,1) * v(1:lastv,1)**H
221*
222 CALL cgerc( lastc, lastv, -tau, work, 1, v, incv, c, ldc )
223 END IF
224 END IF
225 RETURN
226*
227* End of CLARF
228*
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
subroutine cgemv(TRANS, M, N, ALPHA, A, LDA, X, INCX, BETA, Y, INCY)
CGEMV
Definition: cgemv.f:158
subroutine cgerc(M, N, ALPHA, X, INCX, Y, INCY, A, LDA)
CGERC
Definition: cgerc.f:130
integer function ilaclr(M, N, A, LDA)
ILACLR scans a matrix for its last non-zero row.
Definition: ilaclr.f:78
integer function ilaclc(M, N, A, LDA)
ILACLC scans a matrix for its last non-zero column.
Definition: ilaclc.f:78
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