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

Download SLATZM + dependencies [TGZ] [ZIP] [TXT]

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 This routine is deprecated and has been replaced by routine SORMRZ.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'
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
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 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
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:55
subroutine saxpy(N, SA, SX, INCX, SY, INCY)
SAXPY
Definition: saxpy.f:91
subroutine scopy(N, SX, INCX, SY, INCY)
SCOPY
Definition: scopy.f:84
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