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# LAPACK-3

## man page of LAPACK-3

### LAPACK-3: applies a complex block reflector H or its transpose H**H to a complex distributed M-by-N C from the left or the right

```NAME
LAPACK-3 - applies a complex block reflector H or its transpose H**H to
a complex distributed M-by-N C from the left or the right

SYNOPSIS
SUBROUTINE ZLARZB( SIDE, TRANS, DIRECT, STOREV, M, N, K, L, V, LDV,  T,
LDT, C, LDC, WORK, LDWORK )

CHARACTER      DIRECT, SIDE, STOREV, TRANS

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

COMPLEX*16     C( LDC, * ), T( LDT, * ), V( LDV, * ), WORK( LDWORK,
* )

PURPOSE
ZLARZB applies a complex block reflector H or its transpose H**H  to  a
complex distributed M-by-N  C from the left or the right.
Currently, only STOREV = 'R' and DIRECT = 'B' are supported.

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, not supported yet)
= '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                        (not supported yet)
= '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).

L       (input) INTEGER
The number of columns of the matrix V containing the
meaningful part of the Householder reflectors.
If SIDE = 'L', M >= L >= 0, if SIDE = 'R', N >= L >= 0.

V       (input) COMPLEX*16 array, dimension (LDV,NV).
If STOREV = 'C', NV = K; if STOREV = 'R', NV = L.

LDV     (input) INTEGER
The leading dimension of the array V.
If STOREV = 'C', LDV >= L; 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).

FURTHER DETAILS
Based on contributions by
A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA

LAPACK routine (version 3.2)     March 2011                       LAPACK-3(3)
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