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.

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

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'

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date

December 2016

Contributors:

A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA

Further Details:

Definition at line 147 of file slarz.f.

*
*  -- LAPACK computational routine (version 3.7.0) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     December 2016
*
*     .. Scalar Arguments ..
      CHARACTER          SIDE
      INTEGER            INCV, L, LDC, M, N
      REAL               TAU
*     ..
*     .. Array Arguments ..
      REAL               C( LDC, * ), V( * ), WORK( * )
*     ..
*
*  =====================================================================
*
*     .. Parameters ..
      REAL               ONE, ZERO
      parameter( one = 1.0e+0, zero = 0.0e+0 )
*     ..
*     .. External Subroutines ..
      EXTERNAL           saxpy, scopy, sgemv, sger
*     ..
*     .. External Functions ..
      LOGICAL            LSAME
      EXTERNAL           lsame
*     ..
*     .. Executable Statements ..
*
      IF( lsame( side, 'L' ) ) THEN
*
*        Form  H * C
*
         IF( tau.NE.zero ) THEN
*
*           w( 1:n ) = C( 1, 1:n )
*
            CALL scopy( n, c, ldc, work, 1 )
*
*           w( 1:n ) = w( 1:n ) + C( m-l+1:m, 1:n )**T * v( 1:l )
*
            CALL sgemv( 'Transpose', l, n, one, c( m-l+1, 1 ), ldc, v,
     $                  incv, one, work, 1 )
*
*           C( 1, 1:n ) = C( 1, 1:n ) - tau * w( 1:n )
*
            CALL saxpy( n, -tau, work, 1, c, ldc )
*
*           C( m-l+1:m, 1:n ) = C( m-l+1:m, 1:n ) - ...
*                               tau * v( 1:l ) * w( 1:n )**T
*
            CALL sger( l, n, -tau, v, incv, work, 1, c( m-l+1, 1 ),
     $                 ldc )
         END IF
*
      ELSE
*
*        Form  C * H
*
         IF( tau.NE.zero ) THEN
*
*           w( 1:m ) = C( 1:m, 1 )
*
            CALL scopy( m, c, 1, work, 1 )
*
*           w( 1:m ) = w( 1:m ) + C( 1:m, n-l+1:n, 1:n ) * v( 1:l )
*
            CALL sgemv( 'No transpose', m, l, one, c( 1, n-l+1 ), ldc,
     $                  v, incv, one, work, 1 )
*
*           C( 1:m, 1 ) = C( 1:m, 1 ) - tau * w( 1:m )
*
            CALL saxpy( m, -tau, work, 1, c, 1 )
*
*           C( 1:m, n-l+1:n ) = C( 1:m, n-l+1:n ) - ...
*                               tau * w( 1:m ) * v( 1:l )**T
*
            CALL sger( m, l, -tau, work, 1, v, incv, c( 1, n-l+1 ),
     $                 ldc )
*
         END IF
*
      END IF
*
      RETURN
*
*     End of SLARZ
*

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