.TH ZLARZ 1 "November 2006" " LAPACK routine (version 3.1) " " LAPACK routine (version 3.1) " .SH NAME ZLARZ - a complex elementary reflector H to a complex M-by-N matrix C, from either the left or the right .SH SYNOPSIS .TP 18 SUBROUTINE ZLARZ( SIDE, M, N, L, V, INCV, TAU, C, LDC, WORK ) .TP 18 .ti +4 CHARACTER SIDE .TP 18 .ti +4 INTEGER INCV, L, LDC, M, N .TP 18 .ti +4 COMPLEX*16 TAU .TP 18 .ti +4 COMPLEX*16 C( LDC, * ), V( * ), WORK( * ) .SH PURPOSE ZLARZ applies a complex elementary reflector H to a complex M-by-N matrix C, from either the left or the right. H is represented in the form .br H = I - tau * v * v\(aq .br where tau is a complex scalar and v is a complex vector. .br If tau = 0, then H is taken to be the unit matrix. .br To apply H\(aq (the conjugate transpose of H), supply conjg(tau) instead tau. .br H is a product of k elementary reflectors as returned by ZTZRZF. .SH ARGUMENTS .TP 8 SIDE (input) CHARACTER*1 = \(aqL\(aq: form H * C .br = \(aqR\(aq: form C * H .TP 8 M (input) INTEGER The number of rows of the matrix C. .TP 8 N (input) INTEGER The number of columns of the matrix C. .TP 8 L (input) INTEGER The number of entries of the vector V containing the meaningful part of the Householder vectors. If SIDE = \(aqL\(aq, M >= L >= 0, if SIDE = \(aqR\(aq, N >= L >= 0. .TP 8 V (input) COMPLEX*16 array, dimension (1+(L-1)*abs(INCV)) The vector v in the representation of H as returned by ZTZRZF. V is not used if TAU = 0. .TP 8 INCV (input) INTEGER The increment between elements of v. INCV <> 0. .TP 8 TAU (input) COMPLEX*16 The value tau in the representation of H. .TP 8 C (input/output) COMPLEX*16 array, dimension (LDC,N) On entry, the M-by-N matrix C. On exit, C is overwritten by the matrix H * C if SIDE = \(aqL\(aq, or C * H if SIDE = \(aqR\(aq. .TP 8 LDC (input) INTEGER The leading dimension of the array C. LDC >= max(1,M). .TP 8 WORK (workspace) COMPLEX*16 array, dimension (N) if SIDE = \(aqL\(aq or (M) if SIDE = \(aqR\(aq .SH FURTHER DETAILS Based on contributions by .br A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA