zlarz(3P) Sun Performance Library zlarz(3P)NAMEzlarz - applie 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 * 1 SIDE
DOUBLE COMPLEX TAU
DOUBLE COMPLEX V(*), C(LDC,*), WORK(*)
INTEGER M, N, L, INCV, LDC
SUBROUTINE ZLARZ_64(SIDE, M, N, L, V, INCV, TAU, C, LDC, WORK)
CHARACTER * 1 SIDE
DOUBLE COMPLEX TAU
DOUBLE COMPLEX V(*), C(LDC,*), WORK(*)
INTEGER*8 M, N, L, INCV, LDC
F95 INTERFACE
SUBROUTINE LARZ(SIDE, [M], [N], L, V, [INCV], TAU, C, [LDC], [WORK])
CHARACTER(LEN=1) :: SIDE
COMPLEX(8) :: TAU
COMPLEX(8), DIMENSION(:) :: V, WORK
COMPLEX(8), DIMENSION(:,:) :: C
INTEGER :: M, N, L, INCV, LDC
SUBROUTINE LARZ_64(SIDE, [M], [N], L, V, [INCV], TAU, C, [LDC], [WORK])
CHARACTER(LEN=1) :: SIDE
COMPLEX(8) :: TAU
COMPLEX(8), DIMENSION(:) :: V, WORK
COMPLEX(8), DIMENSION(:,:) :: C
INTEGER(8) :: M, N, L, INCV, LDC
C INTERFACE
#include <sunperf.h>
void zlarz(char side, int m, int n, int l, doublecomplex *v, int incv,
doublecomplex *tau, doublecomplex *c, int ldc);
void zlarz_64(char side, long m, long n, long l, doublecomplex *v, long
incv, doublecomplex *tau, doublecomplex *c, long ldc);
PURPOSEzlarz 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)
= 'L': form H * C
= 'R': form C * H
M (input) The number of rows of the matrix C.
N (input) The number of columns of the matrix C.
L (input) The number of entries of the vector V containing the meaning‐
ful part of the Householder vectors. If SIDE = 'L', M >= L
>= 0, if SIDE = 'R', N >= L >= 0.
V (input) COMPLEX*16 array of 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)
The increment between elements of v. INCV <> 0.
TAU (input)
The value tau in the representation of H.
C (input/output)
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)
The leading dimension of the array C. LDC >= max(1,M).
WORK (workspace)
(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
6 Mar 2009 zlarz(3P)
