1CLARZ(1)                 LAPACK routine (version 3.1)                 CLARZ(1)
2
3
4

NAME

6       CLARZ  - a complex elementary reflector H to a complex M-by-N matrix C,
7       from either the left or the right
8

SYNOPSIS

10       SUBROUTINE CLARZ( SIDE, M, N, L, V, INCV, TAU, C, LDC, WORK )
11
12           CHARACTER     SIDE
13
14           INTEGER       INCV, L, LDC, M, N
15
16           COMPLEX       TAU
17
18           COMPLEX       C( LDC, * ), V( * ), WORK( * )
19

PURPOSE

21       CLARZ applies a complex elementary reflector  H  to  a  complex  M-by-N
22       matrix  C,  from  either the left or the right. H is represented in the
23       form
24
25             H = I - tau * v * v'
26
27       where tau is a complex scalar and v is a complex vector.
28
29       If tau = 0, then H is taken to be the unit matrix.
30
31       To apply H' (the conjugate transpose of H), supply  conjg(tau)  instead
32       tau.
33
34       H is a product of k elementary reflectors as returned by CTZRZF.
35
36

ARGUMENTS

38       SIDE    (input) CHARACTER*1
39               = 'L': form  H * C
40               = 'R': form  C * H
41
42       M       (input) INTEGER
43               The number of rows of the matrix C.
44
45       N       (input) INTEGER
46               The number of columns of the matrix C.
47
48       L       (input) INTEGER
49               The number of entries of the vector V containing the meaningful
50               part of the Householder vectors.  If SIDE = 'L', M >= L  >=  0,
51               if SIDE = 'R', N >= L >= 0.
52
53       V       (input) COMPLEX array, dimension (1+(L-1)*abs(INCV))
54               The  vector v in the representation of H as returned by CTZRZF.
55               V is not used if TAU = 0.
56
57       INCV    (input) INTEGER
58               The increment between elements of v. INCV <> 0.
59
60       TAU     (input) COMPLEX
61               The value tau in the representation of H.
62
63       C       (input/output) COMPLEX array, dimension (LDC,N)
64               On entry, the M-by-N matrix C.  On exit, C  is  overwritten  by
65               the matrix H * C if SIDE = 'L', or C * H if SIDE = 'R'.
66
67       LDC     (input) INTEGER
68               The leading dimension of the array C. LDC >= max(1,M).
69
70       WORK    (workspace) COMPLEX array, dimension
71               (N) if SIDE = 'L' or (M) if SIDE = 'R'
72

FURTHER DETAILS

74       Based on contributions by
75         A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA
76
77
78
79
80 LAPACK routine (version 3.1)    November 2006                        CLARZ(1)
Impressum