LAPACK  3.8.0
LAPACK: Linear Algebra PACKage

◆ zlatzm()

subroutine zlatzm ( character  SIDE,
integer  M,
integer  N,
complex*16, dimension( * )  V,
integer  INCV,
complex*16  TAU,
complex*16, dimension( ldc, * )  C1,
complex*16, dimension( ldc, * )  C2,
integer  LDC,
complex*16, dimension( * )  WORK 
)

ZLATZM

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

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 This routine is deprecated and has been replaced by routine ZUNMRZ.

 ZLATZM applies a Householder matrix generated by ZTZRQF to a matrix.

 Let P = I - tau*u*u**H,   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 COMPLEX*16 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 COMPLEX*16
          The value tau in the representation of P.
[in,out]C1
          C1 is COMPLEX*16 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 COMPLEX*16 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 >= max(1,M).
[out]WORK
          WORK is COMPLEX*16 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 154 of file zlatzm.f.

154 *
155 * -- LAPACK computational routine (version 3.7.0) --
156 * -- LAPACK is a software package provided by Univ. of Tennessee, --
157 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
158 * December 2016
159 *
160 * .. Scalar Arguments ..
161  CHARACTER side
162  INTEGER incv, ldc, m, n
163  COMPLEX*16 tau
164 * ..
165 * .. Array Arguments ..
166  COMPLEX*16 c1( ldc, * ), c2( ldc, * ), v( * ), work( * )
167 * ..
168 *
169 * =====================================================================
170 *
171 * .. Parameters ..
172  COMPLEX*16 one, zero
173  parameter( one = ( 1.0d+0, 0.0d+0 ),
174  $ zero = ( 0.0d+0, 0.0d+0 ) )
175 * ..
176 * .. External Subroutines ..
177  EXTERNAL zaxpy, zcopy, zgemv, zgerc, zgeru, zlacgv
178 * ..
179 * .. External Functions ..
180  LOGICAL lsame
181  EXTERNAL lsame
182 * ..
183 * .. Intrinsic Functions ..
184  INTRINSIC min
185 * ..
186 * .. Executable Statements ..
187 *
188  IF( ( min( m, n ).EQ.0 ) .OR. ( tau.EQ.zero ) )
189  $ RETURN
190 *
191  IF( lsame( side, 'L' ) ) THEN
192 *
193 * w := ( C1 + v**H * C2 )**H
194 *
195  CALL zcopy( n, c1, ldc, work, 1 )
196  CALL zlacgv( n, work, 1 )
197  CALL zgemv( 'Conjugate transpose', m-1, n, one, c2, ldc, v,
198  $ incv, one, work, 1 )
199 *
200 * [ C1 ] := [ C1 ] - tau* [ 1 ] * w**H
201 * [ C2 ] [ C2 ] [ v ]
202 *
203  CALL zlacgv( n, work, 1 )
204  CALL zaxpy( n, -tau, work, 1, c1, ldc )
205  CALL zgeru( m-1, n, -tau, v, incv, work, 1, c2, ldc )
206 *
207  ELSE IF( lsame( side, 'R' ) ) THEN
208 *
209 * w := C1 + C2 * v
210 *
211  CALL zcopy( m, c1, 1, work, 1 )
212  CALL zgemv( 'No transpose', m, n-1, one, c2, ldc, v, incv, one,
213  $ work, 1 )
214 *
215 * [ C1, C2 ] := [ C1, C2 ] - tau* w * [ 1 , v**H]
216 *
217  CALL zaxpy( m, -tau, work, 1, c1, 1 )
218  CALL zgerc( m, n-1, -tau, work, 1, v, incv, c2, ldc )
219  END IF
220 *
221  RETURN
222 *
223 * End of ZLATZM
224 *
subroutine zcopy(N, ZX, INCX, ZY, INCY)
ZCOPY
Definition: zcopy.f:83
subroutine zgemv(TRANS, M, N, ALPHA, A, LDA, X, INCX, BETA, Y, INCY)
ZGEMV
Definition: zgemv.f:160
subroutine zgerc(M, N, ALPHA, X, INCX, Y, INCY, A, LDA)
ZGERC
Definition: zgerc.f:132
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:55
subroutine zlacgv(N, X, INCX)
ZLACGV conjugates a complex vector.
Definition: zlacgv.f:76
subroutine zgeru(M, N, ALPHA, X, INCX, Y, INCY, A, LDA)
ZGERU
Definition: zgeru.f:132
subroutine zaxpy(N, ZA, ZX, INCX, ZY, INCY)
ZAXPY
Definition: zaxpy.f:90
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