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# LAPACK-3

## man page of LAPACK-3

### LAPACK-3: applies a complex block reflector H or its transpose H' to a complex M-by-N matrix C, from either the left or the right

```NAME
LAPACK-3 - applies a complex block reflector H or its transpose H' to a
complex M-by-N matrix C, from either the left or the right

SYNOPSIS
SUBROUTINE ZLARFB( 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*16     C( LDC, * ), T( LDT, * ), V( LDV, * ), WORK( LDWORK,
* )

PURPOSE
ZLARFB applies a complex block reflector H or its  transpose  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' from the Left
= 'R': apply H or H' from the Right

TRANS   (input) CHARACTER*1
= 'N': apply H (No transpose)
= 'C': apply 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*16 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*16 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*16 array, dimension (LDC,N)
On entry, the M-by-N matrix C.
On exit, C is overwritten by H*C or H'*C or C*H or C*H'.

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

WORK    (workspace) COMPLEX*16 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).

LAPACK auxiliary routine (versionMarch 2011                       LAPACK-3(3)
```