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## man page of LAPACK-3

### LAPACK-3: applies a complex elementary reflector H to a complex M-by-N matrix C, from either the left or the right

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## NAME

LAPACK-3 - applies a complex elementary reflector H to a complex M-by-N matrix C, from either the left or the right## SYNOPSIS

SUBROUTINE ZLARZ( SIDE, M, N, L, V, INCV, TAU, C, LDC, WORK ) CHARACTER SIDE INTEGER INCV, L, LDC, M, N COMPLEX*16 TAU COMPLEX*16 C( LDC, * ), V( * ), WORK( * )## 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 H = I - tau * v * v' where tau is a complex scalar and v is a complex vector. If tau = 0, then H is taken to be the unit matrix. To apply H' (the conjugate transpose of H), supply conjg(tau) instead tau. H is a product of k elementary reflectors as returned by ZTZRZF.ARGUMENTS

SIDE (input) CHARACTER*1 = 'L': form H * C = 'R': form C * H M (input) INTEGER The number of rows of the matrix C. N (input) INTEGER The number of columns of the matrix C. L (input) INTEGER The number of entries of the vector V containing the meaningful part of the Householder vectors. If SIDE = 'L', M >= L >= 0, if SIDE = 'R', N >= L >= 0. 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. INCV (input) INTEGER The increment between elements of v. INCV <> 0. TAU (input) COMPLEX*16 The value tau in the representation of H. 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 = 'L', or C * H if SIDE = 'R'. LDC (input) INTEGER The leading dimension of the array C. LDC >= max(1,M). WORK (workspace) COMPLEX*16 array, dimension (N) if SIDE = 'L' or (M) if SIDE = 'R'## FURTHER DETAILS

Based on contributions by A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA LAPACK routine (version 3.2) March 2011 LAPACK-3(3)

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