1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
|
.TH CLARZ l "15 June 2000" "LAPACK version 3.0" ")"
.SH NAME
CLARZ - applie 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 CLARZ(
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
TAU
.TP 18
.ti +4
COMPLEX
C( LDC, * ), V( * ), WORK( * )
.SH PURPOSE
CLARZ 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'
.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' (the conjugate transpose of H), supply conjg(tau) instead
tau.
.br
H is a product of k elementary reflectors as returned by CTZRZF.
.SH ARGUMENTS
.TP 8
SIDE (input) CHARACTER*1
= 'L': form H * C
.br
= 'R': 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 = 'L', M >= L >= 0, if SIDE = 'R', N >= L >= 0.
.TP 8
V (input) COMPLEX array, dimension (1+(L-1)*abs(INCV))
The vector v in the representation of H as returned by
CTZRZF. 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 = 'L',
or C * H if SIDE = 'R'.
.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 = 'L'
or (M) if SIDE = 'R'
.SH FURTHER DETAILS
Based on contributions by
.br
A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA
|
