subroutine slarf	(	character	SIDE,
		integer	M,
		integer	N,
		real, dimension( * )	V,
		integer	INCV,
		real	TAU,
		real, dimension( ldc, * )	C,
		integer	LDC,
		real, dimension( * )	WORK
	)

SLARF applies an elementary reflector to a general rectangular matrix.

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

Purpose:

 SLARF 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.

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]	V	V is REAL array, dimension (1 + (M-1)*abs(INCV)) if SIDE = 'L' or (1 + (N-1)*abs(INCV)) if SIDE = 'R' The vector v in the representation of H. 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

September 2012

Definition at line 126 of file slarf.f.

*
*  -- LAPACK auxiliary routine (version 3.4.2) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     September 2012
*
*     .. Scalar Arguments ..
      CHARACTER          side
      INTEGER            incv, 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 )
*     ..
*     .. Local Scalars ..
      LOGICAL            applyleft
      INTEGER            i, lastv, lastc
*     ..
*     .. External Subroutines ..
      EXTERNAL           sgemv, sger
*     ..
*     .. External Functions ..
      LOGICAL            lsame
      INTEGER            ilaslr, ilaslc
      EXTERNAL           lsame, ilaslr, ilaslc
*     ..
*     .. Executable Statements ..
*
      applyleft = lsame( side, 'L' )
      lastv = 0
      lastc = 0
      IF( tau.NE.zero ) THEN
!     Set up variables for scanning V.  LASTV begins pointing to the end
!     of V.
         IF( applyleft ) THEN
            lastv = m
         ELSE
            lastv = n
         END IF
         IF( incv.GT.0 ) THEN
            i = 1 + (lastv-1) * incv
         ELSE
            i = 1
         END IF
!     Look for the last non-zero row in V.
         DO WHILE( lastv.GT.0 .AND. v( i ).EQ.zero )
            lastv = lastv - 1
            i = i - incv
         END DO
         IF( applyleft ) THEN
!     Scan for the last non-zero column in C(1:lastv,:).
            lastc = ilaslc(lastv, n, c, ldc)
         ELSE
!     Scan for the last non-zero row in C(:,1:lastv).
            lastc = ilaslr(m, lastv, c, ldc)
         END IF
      END IF
!     Note that lastc.eq.0 renders the BLAS operations null; no special
!     case is needed at this level.
      IF( applyleft ) THEN
*
*        Form  H * C
*
         IF( lastv.GT.0 ) THEN
*
*           w(1:lastc,1) := C(1:lastv,1:lastc)**T * v(1:lastv,1)
*
            CALL sgemv( 'Transpose', lastv, lastc, one, c, ldc, v, incv,
     $           zero, work, 1 )
*
*           C(1:lastv,1:lastc) := C(...) - v(1:lastv,1) * w(1:lastc,1)**T
*
            CALL sger( lastv, lastc, -tau, v, incv, work, 1, c, ldc )
         END IF
      ELSE
*
*        Form  C * H
*
         IF( lastv.GT.0 ) THEN
*
*           w(1:lastc,1) := C(1:lastc,1:lastv) * v(1:lastv,1)
*
            CALL sgemv( 'No transpose', lastc, lastv, one, c, ldc,
     $           v, incv, zero, work, 1 )
*
*           C(1:lastc,1:lastv) := C(...) - w(1:lastc,1) * v(1:lastv,1)**T
*
            CALL sger( lastc, lastv, -tau, work, 1, v, incv, c, ldc )
         END IF
      END IF
      RETURN
*
*     End of SLARF
*

Here is the call graph for this function:

Here is the caller graph for this function: