.TH CLARF 1 "November 2006" " LAPACK auxiliary routine (version 3.1) " " LAPACK auxiliary routine (version 3.1) " .SH NAME CLARF - 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 CLARF( SIDE, M, N, V, INCV, TAU, C, LDC, WORK ) .TP 18 .ti +4 CHARACTER SIDE .TP 18 .ti +4 INTEGER INCV, LDC, M, N .TP 18 .ti +4 COMPLEX TAU .TP 18 .ti +4 COMPLEX C( LDC, * ), V( * ), WORK( * ) .SH PURPOSE CLARF 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 .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 V (input) COMPLEX array, dimension (1 + (M-1)*abs(INCV)) if SIDE = \(aqL\(aq or (1 + (N-1)*abs(INCV)) if SIDE = \(aqR\(aq The vector v in the representation of H. 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 The value tau in the representation of H. .TP 8 C (input/output) COMPLEX 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 array, dimension (N) if SIDE = \(aqL\(aq or (M) if SIDE = \(aqR\(aq