 LAPACK  3.10.1 LAPACK: Linear Algebra PACKage

## ◆ 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.

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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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