---
name: "clarzb"
section: "3lapack"
platform: "linux"
package: "liblapack-doc"
version: "3.2.1-8"
release: "Debian 6.0 (Squeeze)"
platforms: ["linux"]
url: "https://new.carta.tech/clarzb/3lapack"
---

# clarzb(3lapack)

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

CLARZB - 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 CLARZB(

  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

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

## PURPOSE

CLARZB 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 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 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'\*C or C\*H or C\*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).

## FURTHER DETAILS

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