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