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

 subroutine slarz ( character SIDE, integer M, integer N, integer L, real, dimension( * ) V, integer INCV, real TAU, real, dimension( ldc, * ) C, integer LDC, real, dimension( * ) WORK )

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

Purpose:
``` SLARZ 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.

H is a product of k elementary reflectors as returned by STZRZF.```
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 REAL array, dimension (1+(L-1)*abs(INCV)) The vector v in the representation of H as returned by STZRZF. V is not used if TAU = 0.``` [in] INCV ``` INCV is INTEGER The increment between elements of v. INCV <> 0.``` [in] TAU ``` TAU is REAL The value tau in the representation of H.``` [in,out] C ``` C is REAL 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 REAL 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 144 of file slarz.f.

145*
146* -- LAPACK computational routine --
147* -- LAPACK is a software package provided by Univ. of Tennessee, --
148* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
149*
150* .. Scalar Arguments ..
151 CHARACTER SIDE
152 INTEGER INCV, L, LDC, M, N
153 REAL TAU
154* ..
155* .. Array Arguments ..
156 REAL C( LDC, * ), V( * ), WORK( * )
157* ..
158*
159* =====================================================================
160*
161* .. Parameters ..
162 REAL ONE, ZERO
163 parameter( one = 1.0e+0, zero = 0.0e+0 )
164* ..
165* .. External Subroutines ..
166 EXTERNAL saxpy, scopy, sgemv, sger
167* ..
168* .. External Functions ..
169 LOGICAL LSAME
170 EXTERNAL lsame
171* ..
172* .. Executable Statements ..
173*
174 IF( lsame( side, 'L' ) ) THEN
175*
176* Form H * C
177*
178 IF( tau.NE.zero ) THEN
179*
180* w( 1:n ) = C( 1, 1:n )
181*
182 CALL scopy( n, c, ldc, work, 1 )
183*
184* w( 1:n ) = w( 1:n ) + C( m-l+1:m, 1:n )**T * v( 1:l )
185*
186 CALL sgemv( 'Transpose', l, n, one, c( m-l+1, 1 ), ldc, v,
187 \$ incv, one, work, 1 )
188*
189* C( 1, 1:n ) = C( 1, 1:n ) - tau * w( 1:n )
190*
191 CALL saxpy( n, -tau, work, 1, c, ldc )
192*
193* C( m-l+1:m, 1:n ) = C( m-l+1:m, 1:n ) - ...
194* tau * v( 1:l ) * w( 1:n )**T
195*
196 CALL sger( l, n, -tau, v, incv, work, 1, c( m-l+1, 1 ),
197 \$ ldc )
198 END IF
199*
200 ELSE
201*
202* Form C * H
203*
204 IF( tau.NE.zero ) THEN
205*
206* w( 1:m ) = C( 1:m, 1 )
207*
208 CALL scopy( m, c, 1, work, 1 )
209*
210* w( 1:m ) = w( 1:m ) + C( 1:m, n-l+1:n, 1:n ) * v( 1:l )
211*
212 CALL sgemv( 'No transpose', m, l, one, c( 1, n-l+1 ), ldc,
213 \$ v, incv, one, work, 1 )
214*
215* C( 1:m, 1 ) = C( 1:m, 1 ) - tau * w( 1:m )
216*
217 CALL saxpy( m, -tau, work, 1, c, 1 )
218*
219* C( 1:m, n-l+1:n ) = C( 1:m, n-l+1:n ) - ...
220* tau * w( 1:m ) * v( 1:l )**T
221*
222 CALL sger( m, l, -tau, work, 1, v, incv, c( 1, n-l+1 ),
223 \$ ldc )
224*
225 END IF
226*
227 END IF
228*
229 RETURN
230*
231* End of SLARZ
232*
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
subroutine scopy(N, SX, INCX, SY, INCY)
SCOPY
Definition: scopy.f:82
subroutine saxpy(N, SA, SX, INCX, SY, INCY)
SAXPY
Definition: saxpy.f:89
subroutine sger(M, N, ALPHA, X, INCX, Y, INCY, A, LDA)
SGER
Definition: sger.f:130
subroutine sgemv(TRANS, M, N, ALPHA, A, LDA, X, INCX, BETA, Y, INCY)
SGEMV
Definition: sgemv.f:156
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