dlarfb.f File Reference

Functions/Subroutines
subroutine	dlarfb (side, trans, direct, storev, m, n, k, v, ldv, t, ldt, c, ldc, work, ldwork)
	DLARFB

Function/Subroutine Documentation

dlarfb()

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

DLARFB

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Purpose:

 DLARFB 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).
[in]	V	V is DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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.

Date

November 2011

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 elements equal to 1 are not stored; the corresponding
  array elements are modified but restored on exit. The rest of the
  array is not used.

  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 )