# dlarfb.f

Section: LAPACK (3)
Updated: Tue Nov 14 2017
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dlarfb.f

## SYNOPSIS

### Functions/Subroutines

subroutine dlarfb (SIDE, TRANS, DIRECT, STOREV, M, N, K, V, LDV, T, LDT, C, LDC, WORK, LDWORK)
DLARFB applies a block reflector or its transpose to a general rectangular matrix.

## Function/Subroutine Documentation

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

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:

SIDE

SIDE is CHARACTER*1
= 'L': apply H or H**T from the Left
= 'R': apply H or H**T from the Right

TRANS

TRANS is CHARACTER*1
= 'N': apply H (No transpose)
= 'T': apply H**T (Transpose)

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)

STOREV

STOREV is CHARACTER*1
Indicates how the vectors which define the elementary
reflectors are stored:
= 'C': Columnwise
= 'R': Rowwise

M

M is INTEGER
The number of rows of the matrix C.

N

N is INTEGER
The number of columns of the matrix C.

K

K is INTEGER
The order of the matrix T (= the number of elementary
reflectors whose product defines the block reflector).

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.

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.

T

T is DOUBLE PRECISION array, dimension (LDT,K)
The triangular k by k matrix T in the representation of the
block reflector.

LDT

LDT is INTEGER
The leading dimension of the array T. LDT >= K.

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.

LDC

LDC is INTEGER
The leading dimension of the array C. LDC >= max(1,M).

WORK

WORK is DOUBLE PRECISION array, dimension (LDWORK,K)

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

NAG Ltd.

Date:

June 2013

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 )

Definition at line 197 of file dlarfb.f.

## Author

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