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

 subroutine slatzm ( character SIDE, integer M, integer N, real, dimension( * ) V, integer INCV, real TAU, real, dimension( ldc, * ) C1, real, dimension( ldc, * ) C2, integer LDC, real, dimension( * ) WORK )

SLATZM

Purpose:
``` This routine is deprecated and has been replaced by routine SORMRZ.

SLATZM applies a Householder matrix generated by STZRQF to a matrix.

Let P = I - tau*u*u**T,   u = ( 1 ),
( v )
where v is an (m-1) vector if SIDE = 'L', or a (n-1) vector if
SIDE = 'R'.

If SIDE equals 'L', let
C = [ C1 ] 1
[ C2 ] m-1
n
Then C is overwritten by P*C.

If SIDE equals 'R', let
C = [ C1, C2 ] m
1  n-1
Then C is overwritten by C*P.```
Parameters
 [in] SIDE ``` SIDE is CHARACTER*1 = 'L': form P * C = 'R': form C * P``` [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 REAL array, dimension (1 + (M-1)*abs(INCV)) if SIDE = 'L' (1 + (N-1)*abs(INCV)) if SIDE = 'R' The vector v in the representation of P. 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 P.``` [in,out] C1 ``` C1 is REAL array, dimension (LDC,N) if SIDE = 'L' (M,1) if SIDE = 'R' On entry, the n-vector C1 if SIDE = 'L', or the m-vector C1 if SIDE = 'R'. On exit, the first row of P*C if SIDE = 'L', or the first column of C*P if SIDE = 'R'.``` [in,out] C2 ``` C2 is REAL array, dimension (LDC, N) if SIDE = 'L' (LDC, N-1) if SIDE = 'R' On entry, the (m - 1) x n matrix C2 if SIDE = 'L', or the m x (n - 1) matrix C2 if SIDE = 'R'. On exit, rows 2:m of P*C if SIDE = 'L', or columns 2:m of C*P if SIDE = 'R'.``` [in] LDC ``` LDC is INTEGER The leading dimension of the arrays C1 and C2. LDC >= (1,M).``` [out] WORK ``` WORK is REAL array, dimension (N) if SIDE = 'L' (M) if SIDE = 'R'```

Definition at line 150 of file slatzm.f.

151*
152* -- LAPACK computational routine --
153* -- LAPACK is a software package provided by Univ. of Tennessee, --
154* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
155*
156* .. Scalar Arguments ..
157 CHARACTER SIDE
158 INTEGER INCV, LDC, M, N
159 REAL TAU
160* ..
161* .. Array Arguments ..
162 REAL C1( LDC, * ), C2( LDC, * ), V( * ), WORK( * )
163* ..
164*
165* =====================================================================
166*
167* .. Parameters ..
168 REAL ONE, ZERO
169 parameter( one = 1.0e+0, zero = 0.0e+0 )
170* ..
171* .. External Subroutines ..
172 EXTERNAL saxpy, scopy, sgemv, sger
173* ..
174* .. External Functions ..
175 LOGICAL LSAME
176 EXTERNAL lsame
177* ..
178* .. Intrinsic Functions ..
179 INTRINSIC min
180* ..
181* .. Executable Statements ..
182*
183 IF( ( min( m, n ).EQ.0 ) .OR. ( tau.EQ.zero ) )
184 \$ RETURN
185*
186 IF( lsame( side, 'L' ) ) THEN
187*
188* w := (C1 + v**T * C2)**T
189*
190 CALL scopy( n, c1, ldc, work, 1 )
191 CALL sgemv( 'Transpose', m-1, n, one, c2, ldc, v, incv, one,
192 \$ work, 1 )
193*
194* [ C1 ] := [ C1 ] - tau* [ 1 ] * w**T
195* [ C2 ] [ C2 ] [ v ]
196*
197 CALL saxpy( n, -tau, work, 1, c1, ldc )
198 CALL sger( m-1, n, -tau, v, incv, work, 1, c2, ldc )
199*
200 ELSE IF( lsame( side, 'R' ) ) THEN
201*
202* w := C1 + C2 * v
203*
204 CALL scopy( m, c1, 1, work, 1 )
205 CALL sgemv( 'No transpose', m, n-1, one, c2, ldc, v, incv, one,
206 \$ work, 1 )
207*
208* [ C1, C2 ] := [ C1, C2 ] - tau* w * [ 1 , v**T]
209*
210 CALL saxpy( m, -tau, work, 1, c1, 1 )
211 CALL sger( m, n-1, -tau, work, 1, v, incv, c2, ldc )
212 END IF
213*
214 RETURN
215*
216* End of SLATZM
217*
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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