DLARZB(3) applies a real block reflector H or its transpose H**T to a real distributed M-by-N C from the left or the right

## SYNOPSIS

SUBROUTINE DLARZB(
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

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

## PURPOSE

DLARZB applies a real block reflector H or its transpose H**T to a real 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' (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) DOUBLE PRECISION 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) DOUBLE PRECISION 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) DOUBLE PRECISION 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) DOUBLE PRECISION 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