# zlarfb(3) [debian man page]

```zlarfb.f(3)							      LAPACK							       zlarfb.f(3)

NAME
zlarfb.f -

SYNOPSIS
Functions/Subroutines
subroutine zlarfb (SIDE, TRANS, DIRECT, STOREV, M, N, K, V, LDV, T, LDT, C, LDC, WORK, LDWORK)
ZLARFB

Function/Subroutine Documentation
subroutine zlarfb (characterSIDE, characterTRANS, characterDIRECT, characterSTOREV, integerM, integerN, integerK, complex*16, dimension( ldv, *
)V, integerLDV, complex*16, dimension( ldt, * )T, integerLDT, complex*16, dimension( ldc, * )C, integerLDC, complex*16, dimension( ldwork,
* )WORK, integerLDWORK)
ZLARFB

Purpose:

ZLARFB applies a complex block reflector H or its transpose H**H to a
complex M-by-N matrix C, from either the left or the right.

Parameters:
SIDE

SIDE is CHARACTER*1
= 'L': apply H or H**H from the Left
= 'R': apply H or H**H from the Right

TRANS

TRANS is CHARACTER*1
= 'N': apply H (No transpose)
= 'C': apply H**H (Conjugate 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 COMPLEX*16 array, dimension
(LDV,K) if STOREV = 'C'
(LDV,M) if STOREV = 'R' and SIDE = 'L'
(LDV,N) if STOREV = 'R' and SIDE = 'R'
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 COMPLEX*16 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 COMPLEX*16 array, dimension (LDC,N)
On entry, the M-by-N matrix C.
On exit, C is overwritten by H*C or H**H*C or C*H or C*H**H.

LDC

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

WORK

WORK is COMPLEX*16 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:
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 )

Definition at line 195 of file zlarfb.f.

Author
Generated automatically by Doxygen for LAPACK from the source code.

Version 3.4.1							  Sun May 26 2013						       zlarfb.f(3)```
Man Page