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
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
|
SUBROUTINE DLARZ( SIDE, M, N, L, V, INCV, TAU, C, LDC, WORK )
*
* -- LAPACK routine (version 3.2) --
* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
* November 2006
*
* .. Scalar Arguments ..
CHARACTER SIDE
INTEGER INCV, L, LDC, M, N
DOUBLE PRECISION TAU
* ..
* .. Array Arguments ..
DOUBLE PRECISION C( LDC, * ), V( * ), WORK( * )
* ..
*
* Purpose
* =======
*
* DLARZ applies a real elementary reflector H to a real 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 real scalar and v is a real vector.
*
* If tau = 0, then H is taken to be the unit matrix.
*
*
* H is a product of k elementary reflectors as returned by DTZRZF.
*
* 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) DOUBLE PRECISION array, dimension (1+(L-1)*abs(INCV))
* The vector v in the representation of H as returned by
* DTZRZF. V is not used if TAU = 0.
*
* INCV (input) INTEGER
* The increment between elements of v. INCV <> 0.
*
* TAU (input) DOUBLE PRECISION
* The value tau in the representation of H.
*
* C (input/output) DOUBLE PRECISION 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) DOUBLE PRECISION 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
*
* =====================================================================
*
* .. Parameters ..
DOUBLE PRECISION ONE, ZERO
PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
* ..
* .. External Subroutines ..
EXTERNAL DAXPY, DCOPY, DGEMV, DGER
* ..
* .. External Functions ..
LOGICAL LSAME
EXTERNAL LSAME
* ..
* .. Executable Statements ..
*
IF( LSAME( SIDE, 'L' ) ) THEN
*
* Form H * C
*
IF( TAU.NE.ZERO ) THEN
*
* w( 1:n ) = C( 1, 1:n )
*
CALL DCOPY( N, C, LDC, WORK, 1 )
*
* w( 1:n ) = w( 1:n ) + C( m-l+1:m, 1:n )' * v( 1:l )
*
CALL DGEMV( 'Transpose', L, N, ONE, C( M-L+1, 1 ), LDC, V,
$ INCV, ONE, WORK, 1 )
*
* C( 1, 1:n ) = C( 1, 1:n ) - tau * w( 1:n )
*
CALL DAXPY( N, -TAU, WORK, 1, C, LDC )
*
* C( m-l+1:m, 1:n ) = C( m-l+1:m, 1:n ) - ...
* tau * v( 1:l ) * w( 1:n )'
*
CALL DGER( L, N, -TAU, V, INCV, WORK, 1, C( M-L+1, 1 ),
$ LDC )
END IF
*
ELSE
*
* Form C * H
*
IF( TAU.NE.ZERO ) THEN
*
* w( 1:m ) = C( 1:m, 1 )
*
CALL DCOPY( M, C, 1, WORK, 1 )
*
* w( 1:m ) = w( 1:m ) + C( 1:m, n-l+1:n, 1:n ) * v( 1:l )
*
CALL DGEMV( 'No transpose', M, L, ONE, C( 1, N-L+1 ), LDC,
$ V, INCV, ONE, WORK, 1 )
*
* C( 1:m, 1 ) = C( 1:m, 1 ) - tau * w( 1:m )
*
CALL DAXPY( M, -TAU, WORK, 1, C, 1 )
*
* C( 1:m, n-l+1:n ) = C( 1:m, n-l+1:n ) - ...
* tau * w( 1:m ) * v( 1:l )'
*
CALL DGER( M, L, -TAU, WORK, 1, V, INCV, C( 1, N-L+1 ),
$ LDC )
*
END IF
*
END IF
*
RETURN
*
* End of DLARZ
*
END
|
