Provided by: liblapack-doc_3.3.1-1_all

#### NAME

```       LAPACK-3  -  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

```

#### SYNOPSIS

```       SUBROUTINE CLARFB( SIDE, TRANS, DIRECT, STOREV, M, N, K, V, LDV, T,  LDT,  C,  LDC,  WORK,
LDWORK )

IMPLICIT       NONE

CHARACTER      DIRECT, SIDE, STOREV, TRANS

INTEGER        K, LDC, LDT, LDV, LDWORK, M, N

COMPLEX        C( LDC, * ), T( LDT, * ), V( LDV, * ), WORK( LDWORK, * )

```

#### PURPOSE

```       CLARFB  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.

```

#### ARGUMENTS

```        SIDE    (input) CHARACTER*1
= 'L': apply H or H**H from the Left
= 'R': apply H or H**H from the Right

TRANS   (input) CHARACTER*1
= 'N': apply H (No transpose)
= 'C': apply H**H (Conjugate transpose)

DIRECT  (input) 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  (input) CHARACTER*1
Indicates how the vectors which define the elementary
reflectors are stored:
= 'C': Columnwise
= 'R': Rowwise

M       (input) INTEGER
The number of rows of the matrix C.

N       (input) INTEGER
The number of columns of the matrix C.

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

V       (input) COMPLEX 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     (input) 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       (input) COMPLEX array, dimension (LDT,K)
The triangular K-by-K matrix T in the representation of the
block reflector.

LDT     (input) INTEGER
The leading dimension of the array T. LDT >= K.

C       (input/output) COMPLEX 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     (input) INTEGER
The leading dimension of the array C. LDC >= max(1,M).

WORK    (workspace) COMPLEX array, dimension (LDWORK,K)

LDWORK  (input) INTEGER
The leading dimension of the array WORK.
If SIDE = 'L', LDWORK >= max(1,N);
if SIDE = 'R', LDWORK >= max(1,M).

```

#### FURTHERDETAILS

```        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 )

LAPACK auxiliary routine (version 3.3.1)   April 2011                            CLARFB(3lapack)
```