slarfb()

subroutine slarfb	(	character	side,
		character	trans,
		character	direct,
		character	storev,
		integer	m,
		integer	n,
		integer	k,
		real, dimension( ldv, * )	v,
		integer	ldv,
		real, dimension( ldt, * )	t,
		integer	ldt,
		real, dimension( ldc, * )	c,
		integer	ldc,
		real, dimension( ldwork, * )	work,
		integer	ldwork )

SLARFB applies a block reflector or its transpose to a general rectangular matrix.

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Purpose:

!>
!> SLARFB applies a real block reflector H or its transpose H**T to a
!> real m by n matrix C, from either the left or the right.
!> 

Parameters

[in]	SIDE	!> SIDE is CHARACTER*1 !> = 'L': apply H or H**T from the Left !> = 'R': apply H or H**T from the Right !>
[in]	TRANS	!> TRANS is CHARACTER*1 !> = 'N': apply H (No transpose) !> = 'T': apply H**T (Transpose) !>
[in]	DIRECT	!> DIRECT is CHARACTER*1 !> Indicates how H is formed from a product of elementary !> reflectors !> = 'F': H = H(1) H(2) . . . H(k) (Forward) !> = 'B': H = H(k) . . . H(2) H(1) (Backward) !>
[in]	STOREV	!> STOREV is CHARACTER*1 !> Indicates how the vectors which define the elementary !> reflectors are stored: !> = 'C': Columnwise !> = 'R': Rowwise !>
[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]	K	!> K is INTEGER !> The order of the matrix T (= the number of elementary !> reflectors whose product defines the block reflector). !> If SIDE = 'L', M >= K >= 0; !> if SIDE = 'R', N >= K >= 0. !>
[in]	V	!> V is REAL array, dimension !> (LDV,K) if STOREV = 'C' !> (LDV,M) if STOREV = 'R' and SIDE = 'L' !> (LDV,N) if STOREV = 'R' and SIDE = 'R' !> The matrix V. See Further Details. !>
[in]	LDV	!> LDV is INTEGER !> The leading dimension of the array V. !> If STOREV = 'C' and SIDE = 'L', LDV >= max(1,M); !> if STOREV = 'C' and SIDE = 'R', LDV >= max(1,N); !> if STOREV = 'R', LDV >= K. !>
[in]	T	!> T is REAL array, dimension (LDT,K) !> The triangular k by k matrix T in the representation of the !> block reflector. !>
[in]	LDT	!> LDT is INTEGER !> The leading dimension of the array T. LDT >= K. !>
[in,out]	C	!> C is REAL array, dimension (LDC,N) !> On entry, the m by n matrix C. !> On exit, C is overwritten by H*C or H**T*C or C*H or C*H**T. !>
[in]	LDC	!> LDC is INTEGER !> The leading dimension of the array C. LDC >= max(1,M). !>
[out]	WORK	!> WORK is REAL array, dimension (LDWORK,K) !>
[in]	LDWORK	!> LDWORK is INTEGER !> The leading dimension of the array WORK. !> If SIDE = 'L', LDWORK >= max(1,N); !> if SIDE = 'R', LDWORK >= max(1,M). !>

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Further Details:

!>
!>  The shape of the matrix V and the storage of the vectors which define
!>  the H(i) is best illustrated by the following example with n = 5 and
!>  k = 3. The triangular part of V (including its diagonal) is not
!>  referenced.
!>
!>  DIRECT = 'F' and STOREV = 'C':         DIRECT = 'F' and STOREV = 'R':
!>
!>               V = (  1       )                 V = (  1 v1 v1 v1 v1 )
!>                   ( v1  1    )                     (     1 v2 v2 v2 )
!>                   ( v1 v2  1 )                     (        1 v3 v3 )
!>                   ( v1 v2 v3 )
!>                   ( v1 v2 v3 )
!>
!>  DIRECT = 'B' and STOREV = 'C':         DIRECT = 'B' and STOREV = 'R':
!>
!>               V = ( v1 v2 v3 )                 V = ( v1 v1  1       )
!>                   ( v1 v2 v3 )                     ( v2 v2 v2  1    )
!>                   (  1 v2 v3 )                     ( v3 v3 v3 v3  1 )
!>                   (     1 v3 )
!>                   (        1 )
!>