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

 subroutine dlarf ( character SIDE, integer M, integer N, double precision, dimension( * ) V, integer INCV, double precision TAU, double precision, dimension( ldc, * ) C, integer LDC, double precision, dimension( * ) WORK )

DLARF applies an elementary reflector to a general rectangular matrix.

Purpose:
``` DLARF applies a real elementary reflector H to a real m by n matrix
C, from either the left or the right. H is represented in the form

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

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

If tau = 0, then H is taken to be the unit matrix.```
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 DOUBLE PRECISION 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 DOUBLE PRECISION The value tau in the representation of H.``` [in,out] C ``` C is DOUBLE PRECISION 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 DOUBLE PRECISION array, dimension (N) if SIDE = 'L' or (M) if SIDE = 'R'```

Definition at line 123 of file dlarf.f.

124*
125* -- LAPACK auxiliary routine --
126* -- LAPACK is a software package provided by Univ. of Tennessee, --
127* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
128*
129* .. Scalar Arguments ..
130 CHARACTER SIDE
131 INTEGER INCV, LDC, M, N
132 DOUBLE PRECISION TAU
133* ..
134* .. Array Arguments ..
135 DOUBLE PRECISION C( LDC, * ), V( * ), WORK( * )
136* ..
137*
138* =====================================================================
139*
140* .. Parameters ..
141 DOUBLE PRECISION ONE, ZERO
142 parameter( one = 1.0d+0, zero = 0.0d+0 )
143* ..
144* .. Local Scalars ..
145 LOGICAL APPLYLEFT
146 INTEGER I, LASTV, LASTC
147* ..
148* .. External Subroutines ..
149 EXTERNAL dgemv, dger
150* ..
151* .. External Functions ..
152 LOGICAL LSAME
155* ..
156* .. Executable Statements ..
157*
158 applyleft = lsame( side, 'L' )
159 lastv = 0
160 lastc = 0
161 IF( tau.NE.zero ) THEN
162! Set up variables for scanning V. LASTV begins pointing to the end
163! of V.
164 IF( applyleft ) THEN
165 lastv = m
166 ELSE
167 lastv = n
168 END IF
169 IF( incv.GT.0 ) THEN
170 i = 1 + (lastv-1) * incv
171 ELSE
172 i = 1
173 END IF
174! Look for the last non-zero row in V.
175 DO WHILE( lastv.GT.0 .AND. v( i ).EQ.zero )
176 lastv = lastv - 1
177 i = i - incv
178 END DO
179 IF( applyleft ) THEN
180! Scan for the last non-zero column in C(1:lastv,:).
181 lastc = iladlc(lastv, n, c, ldc)
182 ELSE
183! Scan for the last non-zero row in C(:,1:lastv).
184 lastc = iladlr(m, lastv, c, ldc)
185 END IF
186 END IF
187! Note that lastc.eq.0 renders the BLAS operations null; no special
188! case is needed at this level.
189 IF( applyleft ) THEN
190*
191* Form H * C
192*
193 IF( lastv.GT.0 ) THEN
194*
195* w(1:lastc,1) := C(1:lastv,1:lastc)**T * v(1:lastv,1)
196*
197 CALL dgemv( 'Transpose', lastv, lastc, one, c, ldc, v, incv,
198 \$ zero, work, 1 )
199*
200* C(1:lastv,1:lastc) := C(...) - v(1:lastv,1) * w(1:lastc,1)**T
201*
202 CALL dger( lastv, lastc, -tau, v, incv, work, 1, c, ldc )
203 END IF
204 ELSE
205*
206* Form C * H
207*
208 IF( lastv.GT.0 ) THEN
209*
210* w(1:lastc,1) := C(1:lastc,1:lastv) * v(1:lastv,1)
211*
212 CALL dgemv( 'No transpose', lastc, lastv, one, c, ldc,
213 \$ v, incv, zero, work, 1 )
214*
215* C(1:lastc,1:lastv) := C(...) - w(1:lastc,1) * v(1:lastv,1)**T
216*
217 CALL dger( lastc, lastv, -tau, work, 1, v, incv, c, ldc )
218 END IF
219 END IF
220 RETURN
221*
222* End of DLARF
223*
integer function iladlc(M, N, A, LDA)
ILADLC scans a matrix for its last non-zero column.
integer function iladlr(M, N, A, LDA)
ILADLR scans a matrix for its last non-zero row.
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
subroutine dger(M, N, ALPHA, X, INCX, Y, INCY, A, LDA)
DGER
Definition: dger.f:130
subroutine dgemv(TRANS, M, N, ALPHA, A, LDA, X, INCX, BETA, Y, INCY)
DGEMV
Definition: dgemv.f:156
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