 LAPACK  3.8.0 LAPACK: Linear Algebra PACKage

## ◆ 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``` This routine is deprecated and has been replaced by routine SORMRZ.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'```
Date
December 2016

Definition at line 153 of file slatzm.f.

153 *
154 * -- LAPACK computational routine (version 3.7.0) --
155 * -- LAPACK is a software package provided by Univ. of Tennessee, --
156 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
157 * December 2016
158 *
159 * .. Scalar Arguments ..
160  CHARACTER side
161  INTEGER incv, ldc, m, n
162  REAL tau
163 * ..
164 * .. Array Arguments ..
165  REAL c1( ldc, * ), c2( ldc, * ), v( * ), work( * )
166 * ..
167 *
168 * =====================================================================
169 *
170 * .. Parameters ..
171  REAL one, zero
172  parameter( one = 1.0e+0, zero = 0.0e+0 )
173 * ..
174 * .. External Subroutines ..
175  EXTERNAL saxpy, scopy, sgemv, sger
176 * ..
177 * .. External Functions ..
178  LOGICAL lsame
179  EXTERNAL lsame
180 * ..
181 * .. Intrinsic Functions ..
182  INTRINSIC min
183 * ..
184 * .. Executable Statements ..
185 *
186  IF( ( min( m, n ).EQ.0 ) .OR. ( tau.EQ.zero ) )
187  \$ RETURN
188 *
189  IF( lsame( side, 'L' ) ) THEN
190 *
191 * w := (C1 + v**T * C2)**T
192 *
193  CALL scopy( n, c1, ldc, work, 1 )
194  CALL sgemv( 'Transpose', m-1, n, one, c2, ldc, v, incv, one,
195  \$ work, 1 )
196 *
197 * [ C1 ] := [ C1 ] - tau* [ 1 ] * w**T
198 * [ C2 ] [ C2 ] [ v ]
199 *
200  CALL saxpy( n, -tau, work, 1, c1, ldc )
201  CALL sger( m-1, n, -tau, v, incv, work, 1, c2, ldc )
202 *
203  ELSE IF( lsame( side, 'R' ) ) THEN
204 *
205 * w := C1 + C2 * v
206 *
207  CALL scopy( m, c1, 1, work, 1 )
208  CALL sgemv( 'No transpose', m, n-1, one, c2, ldc, v, incv, one,
209  \$ work, 1 )
210 *
211 * [ C1, C2 ] := [ C1, C2 ] - tau* w * [ 1 , v**T]
212 *
213  CALL saxpy( m, -tau, work, 1, c1, 1 )
214  CALL sger( m, n-1, -tau, work, 1, v, incv, c2, ldc )
215  END IF
216 *
217  RETURN
218 *
219 * End of SLATZM
220 *
subroutine scopy(N, SX, INCX, SY, INCY)
SCOPY
Definition: scopy.f:84
subroutine saxpy(N, SA, SX, INCX, SY, INCY)
SAXPY
Definition: saxpy.f:91
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:55
subroutine sger(M, N, ALPHA, X, INCX, Y, INCY, A, LDA)
SGER
Definition: sger.f:132
subroutine sgemv(TRANS, M, N, ALPHA, A, LDA, X, INCX, BETA, Y, INCY)
SGEMV
Definition: sgemv.f:158
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